This list can be found on github and medium:
https://github.com/memo/ai-resources
https://medium.com/@memoakten/selection-of-resources-to-learn-artificial-intelligence-machine-learning-statistical-inference-23bc56ba655

Update April 2017: It’s been almost a year since I posted this list of resources, and over the year there’s been an explosion of articles, videos, books, tutorials etc on the subject — even an explosion of ‘lists of resources’ such as this one. It’s impossible for me to keep this up to date. However, the one resource I would like to add is https://ml4a.github.io/ (https://github.com/ml4a) led by Gene Kogan. It’s specifically aimed at artists and the creative coding community.

Introduction

This is a very incomplete and subjective selection of resources to learn about the algorithms and maths of Artificial Intelligence (AI) / Machine Learning (ML) / Statistical Inference (SI) / Deep Learning (DL) / Reinforcement Learning (RL). It is aimed at beginners (those without Computer Science background and not knowing anything about these subjects) and hopes to take them to quite advanced levels (able to read and understand DL papers). It is not an exhaustive list and only contains some of the learning materials that I have personally completed so that I can include brief personal comments on them. It is also by no means the best path to follow (nowadays most MOOCs have full paths all the way from basic statistics and linear algebra to ML/DL). But this is the path I took and in a sense it's a partial documentation of my personal journey into DL (actually I bounced around all of these back and forth like crazy). As someone who has no formal background in Computer Science (but has been programming for many years), the language, notation and concepts of ML/SI/DL and even CS was completely alien to me, and the learning curve was not only steep, but vertical, treacherous and slippery like ice.

A lot of the resources below are actually not for DL but more comprehensive ML/SI. DL is mostly just tweaks on top of older techniques, so once you have a solid foundation in ML/SI it makes a lot more sense. If you go through the video lectures below (including advanced ones), you'll be able to pick up current DL developments directly from the published papers.

If you really want to understand AI/ML/SI/DL/RL indepth with all the maths, you need a good understanding of linear algebra (vectors & matrices), probability and statistics (which is more complex than it sounds), and calculus (mainly multivariate differential calculus, which is often simpler than it sounds). I've included lectures for these too. You can't cut corners. Take the time and study as much of the below as you can, from the beginning. Strong foundations are crucial. I often started watching one lecture, 5 minutes in I realized I didn't understand anything so went back to watch another lecture which covered slightly more fundamental topics, 5 minutes in I realized I still didn't understand anything so went back to watch another lecture which covered even more fundamental topics, etc. until I went back 10 lectures. It has been depressing at times (like trying to climb vertical, treacherous, slippery walls of ice without the right tools).

If you just want to use the algorithms without necessarily understanding or delving into the maths, or just want to understand the algorithms at a high conceptual level, that's perfectly fine too. Hopefully my comments below will make it clear what's what.

Tips

There's a lot of overlap in the lectures below. That's a good thing. Don't skip things because you've already read or seen them elsewhere. If you're trying to learn and understand something which is potentially quite complicated, having different people explain the same thing to you in different ways is very useful and often gives insight or intuition you might not otherwise find.

If there are sections which you are 100% comfortable with, then you could watch those sections at 1.25x, 1.5x, or even 2.0x speed just to see what's going on, and then switch back to 1.0x speed once you encounter new material or interesting new angles on the same material.

Video Lectures & Workshops

These are one off video lectures (~1 hour) or workshops (~2-3 hours) that give overviews, intuition or advanced crash courses. You won't learn much about the depths of how things work, but will at least probably understand what things are, what they mean and what you can do with them. These are usually a good intro before you dive into the heavier MOOCs.

Introductory Summaries

Deep Learning by Yann LeCun and Yohua Bengio @ NIPS 2015
http://research.microsoft.com/apps/video/?id=259574
Quite up to date overview of what DL is, how it works (at a very high level) and latest developments, from the grandmasters Yoshua Bengio and Yann LeCun. Bit of an ad for their respective research labs. It's not very technical and doesn't require much maths. Some slides do get a little technical and in those cases if you are familiar with the usual linear algebra / calculus etc you'll get more out of it. If you know nothing (or very little) about AI/ML/DL this course will probably be useful for you and give you an idea of what DL is. If you know ML quite well but not DL then this might be more useful for you.

The Unreasonable Effectiveness of Deep Learning by Yann LeCun 2014
http://videolectures.net/sahd2014_lecun_deep_learning/
Famous lecture by Yannn LeCun, godfather of deep convolutional neural networks (CNN). Brief intro to DL, why it's awesome, and then mainly focuses on CNNs. Very similar to above. Could probably be skipped if you watch the above video.

Deep Learning RNNaissance by Juergen Schmidhuber @ NYC ML Meetup 2014
https://www.youtube.com/watch?v=6bOMf9zr7N8
An alternate history of DL from Jurgen Scmidhuber, another grandmaster of DL. He goes into more detailed history of the algorithms and where they come from, and then focuses on Recurrent Neural Networks (RNN), which his lab made many innovations on (including LSTM). Bit of an ad for his own research lab(s). This video is a bit more advanced than the above ones. Arguably more interesting too.

Basics of Computational Reinforcement Learning by Michael Littman @ RLDM 2015
http://videolectures.net/rldm2015_littman_computational_reinforcement
Kind of an overview intro to RL. Some experience with MDPs etc would be useful but not essential. Michael Littman is one of the old school stars of RL and a lot of fun.

Advanced Crash Courses

Deep Learning by Ruslan Salakhutdinov @ KDD 2014
http://videolectures.net/kdd2014_salakhutdinov_deep_learning
Overview of DL including DBN, RBM, PGM etc which are not as popular these days. Very theoretical, dense and mathematical. Maybe not that useful for beginners. Salakhutdinov is another major player in DL.

Introduction to Reinforcement Learning with Function Approximation by Rich Sutton @ NIPS 2015
http://research.microsoft.com/apps/video/?id=259577
Another intro to RL but more technical and theoretical. Rich Sutton is old school king of RL.

Deep Reinforcement Learning by David Silver @ RLDM 2015
http://videolectures.net/rldm2015_silver_reinforcement_learning
Advanced intro to Deep RL as used by Deepmind on the Atari games and AlphaGo. Quite technical and requires decent understanding of RL, TD learning and Q-Learning etc. (see RL courses below). David Silver is the new school king of RL and superstar of Deepmind's AlphaGo (which uses Deep RL).

Monte Carlo Inference Methods by Ian Murray @ NIPS 2015
http://research.microsoft.com/apps/video/?id=259575
Good introduction and overview of sampling / monte carlo based methods. Not essential for a lot of DL, but good side knowledge to have.

How to Grow a Mind: Statistics, Structure and Abstraction by Josh Tenenbaum @ AAAI 2012
http://videolectures.net/aaai2012_tenenbaum_grow_mind/
Completely unrelated to current DL and takes a very different approach: Bayesian Heirarchical Models. Not much success in real world yet, but I'm still a fan as the questions and problems they're looking at feels a lot more applicable to real world than DL (e.g. one-shot learning and transfer learning, though Deepmind is looking at this with DL as well now).

Two architectures for one-shot learning by Josh Tenenbaum @ NIPS 2013
http://videolectures.net/nipsworkshops2013_tenenbaum_learning
Similar to above but slightly more recent.

Optimal and Suboptimal Control in Brain and Behavior by Nathaniel Daw @ NIPS 2015
http://videolectures.net/rldm2015_daw_brain_and_behavior
Quite unrelated to DL, looks at human learning - combined with research from pyschology and neuroscience - through the computational lens of RL. Requires decent understanding of RL.

Lots more one-off video lectures at:
http://videolectures.net/Top/Computer_Science/Artificial_Intelligence
http://videolectures.net/Top/Computer_Science/Machine_Learning/

Massive Open Online Courses (MOOC)

These are concentrated long term courses consisting of many video lectures. Ordered very roughly in the order that I recommend they are watched.

Foundation / Maths

If you want to understand the maths of ML/SI/DL then these are crucial. If you don't want to understand the maths, but only want to understand the concepts then you could probably skip these and go straight to the introductory ML courses. However, this is also where some of the fundamental terminology is defined (prior, conditional, expected value, derivative, vector, matrix etc). So it helps to at least know what these things mean.

Instead of going through all of these now, you could just watch some of the basic lessons first to help you understand the fundamentals. And then come back to some of the more advanced lessons if and when you encounter them. E.g. it's quite probable that you'll never encounter a Hessian matrix, or require eigenvectors or calculate the determinant of a matrix by hand. And only if and when you do, then you could come back and watch the relevant lessons. You can also skip proofs if you're short on time, but they do help you understand better. Try not to be impatient.

Khan is a superhero and will make you understand things you never knew you could.

Khan Academy - Probability & Statistics
https://www.khanacademy.org/math/probability
ML is basically a subdiscipline of applied statistics mashed with computer science. So basic understanding of probability & statistics is essential. You don't need to watch all lessons, but at least the first few sections to understand the concepts. Bear in mind as you watch the more advanced stuff - which may not be nessecary for ML - they actually help you understand the basic stuff better.

Khan Academy - Linear Algebra
https://www.khanacademy.org/math/linear-algebra
Again you probably don't need to watch them all, but at least vectors, matrics, operations on them, dot & cross product, matrix multiplication etc. is essential for the most basic understanding of ML maths. Basis, eigenvalues/eigenvectors is essential for deeper understanding for some areas, but you could scrape by without them, at least for now.

Khan Academy - Calculus
https://www.khanacademy.org/math/calculus-home
Precalculus - trigonometry, vectors, matrices are essential. If you watched the linear algebra lessons above you may not need this. Complex numbers, sequences and series etc. are useful and come up in various advanced areas, but not nessecary for basics.

Differential Calculus - Essential (esp chain rule) if you want to understand maths of ML. You could skip proofs and the applications if you're impatient, though maxima / minima, concavity & inflection, optimization is important.

Integral Calculus - I don't think integral calculus is integral to DL (see what I did there? :). I've seen it in a few proofs, but it's more of a niche thing I think in ML which beginners could skip for now. Watch at least the first sections to know what it is. Function approximation, series etc. do come up in more advanced areas but safe to skip for now.

Multivariate Calculus - Essential if you really want to understand the maths of DL, especially (partial) derivatives of multivariable functions. Hessians, Jacobians, Laplacians etc come up a lot in advanced areas, but you could get by and understand basic ML without knowing these. I.e. you could skip these for now and come back later, once you encounter them.

Machine Learning / Deep Learning

Short / Introductory Courses

These are probably enough (combined with some tutorials) if you just want to be able to play with and tweak existing ML/DL code and algorithms.

Machine Learning by Andrew Ng @ Coursera
https://www.coursera.org/learn/machine-learning
Fantastic introductory course and foundation for ML. Covers basics of ML from linear and logistic regression to artificial neural networks. Gives great insight into concepts and techniques with minimal maths. Requires basic knowledge of linear algebra and differential calculus. Note: doesn't cover specifities of current deep learning (e.g. convolutional neural networks, recurrent neural networks etc.), so is mainly a great foundation for more advanced studies. Andrew Ng was co-founder of Google Brain and now chief scientist at Baidu research. He is great at giving intuition.

Deep Learning by Google @ Udacity
https://www.udacity.com/course/deep-learning--ud730
Brief introduction to DL for those who are familiar with ML. This is a very short course, I think I went through the whole thing in under 2 hours. It's almost a reading of the tensorflow tutorials ( https://www.tensorflow.org/versions/master/tutorials/index.html ). It gives a top level summary of basic DL techniques. Assumes you're comfortable with ML and related concepts. So at least Andrew Ng's coursera (or equivalent knowledge) is a must. Don't expect to be a DL wizard after this, but at least you might know what a CNN or RNN is. If you're going to look at any of the advanced ML courses below, watch this DL course after them.

Longer / Advanced Courses

These will help you understand what's actually going on, perhaps even understand some DL papers (I say 'some' DL papers because others are just insanely theoretical and dense).

CS188 Introduction to Artificial Intelligence by Pieter Abbeel @ Berkeley
(some videos have audio issues, so below are a bunch of playlists from different years, I had to pick and choose from different playlists depending on audio problems).
https://www.youtube.com/channel/UCDZUttQj8ytfASQIcvsLYgg (Spring 2015)
https://www.youtube.com/channel/UCB4_W1V-KfwpTLxH9jG1_iA (Spring 2014)
https://www.youtube.com/channel/UCshmLD2MsyqAKBx8ctivb5Q (Fall 2013)
https://www.youtube.com/user/CS188Spring2013 (Spring 2013)
This is a fantastic introduction to AI in general, not specifically ML and introduces many different fundamental areas of AI and ML. Spreads the net very wide, so if all you're interested in is playing convolutional neural networks to make things like Deepdream, then 90% of this course won't be relevant. The first half is more agent-based AI starting with CSPs, decision trees, MDPs etc, and in that respect it is a bit unique compared to the other courses on this list. Then goes into various different classic ML topics. It is an introduction, so requires no prior knowledge of AI or ML, but it does go into maths, so requires decent understanding of the usual probability, linear algebra, calculus etc. Doesn't cover DL but a great foundation for a lot of AI and ML, especially if you want to get more into agent-based AI such as RL and Monte Carlo Tree Search (MCTS).

CS540 Machine Learning by Nando de Freitas @ UBC 2013
https://www.youtube.com/playlist?list=PLE6Wd9FR--EdyJ5lbFl8UuGjecvVw66F6
This covers many classic ML and SI etc from start all the way to neural networks. Doesn't require prior knowledge of ML, so can be considered comprehensive introduction. It's way more thorough and detailed than Andrew Ng's Coursera and goes heavy into maths. Bear in mind it's a post-graduate CS course so it's quite advanced. Again spreads the net quite wide, but not as wide as CS188, instead goes deeper into some areas. Only brief intro to DL but comprehensive foundation in ML and SI. Nando is ace. Also prof at Oxford and works for Deepmind.

CS340 Machine Learning by Nando de Freitas @ UBC 2012
https://www.youtube.com/playlist?list=PLE6Wd9FR--Ecf_5nCbnSQMHqORpiChfJf
Similar to above, but undergraduate version. I haven't actually watched these so I don't know how they differ from CS540. Probably bit simpler.

Deep Learning by Nando de Freitas @ Oxford 2015
https://www.youtube.com/playlist?list=PLE6Wd9FR--EfW8dtjAuPoTuPcqmOV53Fu
Similar to CS540 but more about DL. Definitely requires more understanding of statistics and multivariate differential calculus, and prior knowledge in ML/SI (Andrew Ng's coursera may be enough, but I really recommend Nando's CS540 or Pieter's CS188). Even knowledge of information theory would be useful. Great guest lectures by Alex Graves on generative RNNs and Karol Gregor on VAEs.

CS229 Machine Learning by Andrew Ng @ Stanford 2008
https://www.youtube.com/view_play_list?p=A89DCFA6ADACE599
Another very comprehensive introduction to ML/SI. Nothing like his Coursera, way more theoretical and covers lots more topics, and much more thorough. Kind of like a mashup of Pieter Abbeel's CS188 AI Course and Nando de Freitas's CS540 ML Course. This course is more detailed in some areas, and less detailed in others (e.g. AFAIR goes deeper into MDPs and RL than Abbeel's CS188, but doesn't cover bayes nets). They all provide slightly different perspectives and insights. Also doesn't cover DL, just a really solid comprehensive foundation for ML and SI.

Neural Networks for Machine Learning by Geoffrey Hinton @ Coursera
https://www.coursera.org/course/neuralnets
Goes deep into some areas of DL and rather advanced. Hinton is one of the titans of DL and there is a lot of insight in here, but I found it a bit all over the place and I wasn't a huge fan of it. I.e. I don't think it's very useful as a linear educational resource and requies prior knowledge of ML, SI and DL. If you first learn these topics elsewhere (e.g. videos above) and then come back to this course then you can find great insight. Otherwise if you dive straight into this you will get lost.

Computational Neuroscience by Rajesh Rao & Adrienne Fairhall @ Coursera
https://www.coursera.org/course/compneuro
Not directly related to DL but fascinating nevertheless. Starts quite fun but gets rather heavy, especially Adrienne's sections. Rajesh takes things quite slow and re-iterates everything, but I think Adrienne is used to dealing with comp-neuroscience postgrad students and flies through the slides. Expect to pause the video on every slide while you try to digest what's on the screen. Requires decent understanding of the usual suspects, linear algebra, differential calculus, probability and statistical analysis, including things like PCA etc.

I haven't completed, but started or skimmed through

Machine Learning for Musicians and Artists by Rebecca Fiebrink @ Kadenze
https://www.kadenze.com/courses/machine-learning-for-musicians-and-artists/info
Aimed at artists and musicians. I haven't watched this but knowing Rebecca and her work this is bound to ace.

Machine Learning by Georgia Tech (Charles Isbell & Michael Littman) @ Udacity
https://www.udacity.com/course/machine-learning-supervised-learning--ud675
https://www.udacity.com/course/machine-learning-unsupervised-learning--ud741
https://www.udacity.com/course/machine-learning-reinforcement-learning--ud820
Looks like basic introduction to main topics. Doesn't look too heavy. Probably requires basic linear algebra etc but not too complex. Charles Isbell and Michael Littman are really good.

Reinforcement Learning by Michael Littman, Chris Pryby & Charles Isbell @ Udacity
https://www.udacity.com/course/reinforcement-learning--ud600
Did about half of this then got distracted by other things. Similar to above but focuses on MDPs and RL and goes quite thorough. I'd like to finish it but have other priorties right now.

Reinforcement Learning by David Silver @ UCL 2015
http://www0.cs.ucl.ac.uk/staff/d.silver/web/Teaching.html
https://www.youtube.com/playlist?list=PL5X3mDkKaJrL42i_jhE4N-p6E2Ol62Ofa
Introduction to MDPs and RL. Looks lighter and briefer than above. But perhaps enough for most RL explorations. David Silver is superstar of Deepmind's AlphaGo (which uses Deep RL).

Probabilistic Graphical Models by Daphne Koller / Stanfod @ Coursera
https://www.coursera.org/course/pgm
Not actually directly related to DL but probabilistic methods, bayes networks etc. (i.e. related to Josh Tenenbaum's talks at the top). I started this but stopped after a while as I got busy with other things. Starts fun but gets quite heavy. Looks like it's very thorough, perhaps too thorough as it seems to be covering a whole range of topics past and present. I'd like to finish it but have other priorties right now.

Tutorials / Articles / Blogs

There are so many articles & tutorials now, especially tutorials on very specific subjects, that I can't list them all. So below a few main ones that cover broad topics and mainly foundational material. Many of these require some prior knowledge of ML/DL and linear algebra, calculus etc.

Blogs & Unstructured Tutorials

These are sites which have unstructured tutorials on various different topics.

http://colah.github.io
Chris Olah's blog. Lots of great insight on complex topics and concepts.

http://karpathy.github.io
Andrei Karpathy's blog. Similar to above.

http://blog.otoro.net/
@hardmaru's blog. Great explanations of concepts and example code too.

http://fastml.com/
Lots of good examples.

http://blog.keras.io
Tutorials on DL as implemented in Keras, a python based DL framework that sits on top of Tensorflow and Theano.

Linear Tutorials

These are linear tutorials that start from beginning to end.

https://www.tensorflow.org/versions/master/tutorials/index.html
Tutorials on DL as implemented in Tensorflow, Google's python based DL framework. Requires understanding of ML fundamentals, linear algebra, calculus etc.

http://deeplearning.net/tutorial/contents.html
Tutorials on DL as implemented in Theano, a python based DL framework. Requires understanding of ML fundamentals, linear algebra, calculus etc.

Books

Deep Learning by Ian Goodfellow, Yoshua Bengio and Aaron Courville
http://www.deeplearningbook.org
Free online book. Very recent. Briefly covers required maths too.

Information Theory, Inference, and Learning Algorithms by David Mackay
http://www.inference.phy.cam.ac.uk/itprnn/book.html
Free online book. Relatively old (1st 1997, current 2005) but classic textbook. Very statistical and theoretical. Heavy. Requires good understanding of multivariate calculus, linear algebra etc.

Pattern Recognition and Machine Learning by Chris Bishop
http://research.microsoft.com/en-us/um/people/cmbishop/prml
Similar to above (not online or free though). Classic text book. Very theoretical.

Reinforcement Learning: An Introduction by Richard S. Sutton and Andrew G. Barto
https://webdocs.cs.ualberta.ca/~sutton/book/the-book.html
Online book on RL.

The Mathematical Theory of Communication by Claude E. Shannon (1948/1949)
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?reload=true&arnumber=6773024
http://www.amazon.com/Mathematical-Theory-Communication-Claude-Shannon/dp/0252725484
Classic article/book which gives birth to modern Information Theory. I realize I'm on a slippery slope by recommending this as it's originally a paper, and if I suggest this I'd have to suggest a dozen others. But I find this book so useful as a foundation and alternative (supplementary) angle to help understand ML/SI concepts that I couldn't resist it. I actually recommend the book version (as opposed to paper) because it has an additional article by Warren Weaver which explains the concepts in plain English, before Shannon explains them with maths. The maths isn't actually that hairy and mainly requires good understanding of basic probability and Bayes law.

Other Recommendations

These are resources which I have not read or watched, but come highly recommended by others.

Linear Algebra (Video lectures) by Gilbert Strang & MIT
http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/

Machine Learning: a Probabilistic Perspective (Book) by Kevin Patrick Murphy
https://www.cs.ubc.ca/~murphyk/MLbook

Most Cited Deep Learning Papers by Terry Taewoong Um
https://github.com/terryum/awesome-deep-learning-papers
"A curated list of the most cited deep learning papers (since 2010). I believe that there exist classic deep learning papers which are worth reading regardless of their applications. Rather than providing overwhelming amount of papers, I would like to provide a curated list of the classic deep learning papers which can be considered as must-reads in some area."

Critical Algorithm Studies: a Reading List by Tarleton Gillespie and Nick Seaver
https://socialmediacollective.org/reading-lists/critical-algorithm-studies
Not related to the maths/algorithms directly but important nevertheless.
"This list is an attempt to collect and categorize a growing critical literature on algorithms as social concerns. The work included spans sociology, anthropology, science and technology studies, geography, communication, media studies, and legal studies, among others."

Programming Community Curated Resources for Learning AI https://hackr.io/tutorials/learn-artificial-intelligence-ai "Learn Artificial Intelligence (AI) from the best online Artificial Intelligence courses/tutorials submitted and voted by the programming community."

Notes

This is a list of resources that I have personally watched or read, accompanied by my brief thoughts on them, it doesn't make sense for me to accept pull requests (unless there are typos). But. Please do send me suggestions (probably via issues) for others. I have added an 'Other Recommendations' section where I am including other resources which come highly recommended by others.