This blog post accompanies my video on this topic https://youtu.be/Rs572Cf4zkk. This post will contain more information, and I'll keep it updated with answers to FAQs.
This is a pretty serious, and undoubtedly long term project. In fact, I recommend doing it at the pace of a few hours a week rather than all at once to help retain it. I'll be adding study tips here as more people tell me about how they'd like to do this project, so let me know!
Feynman Lectures on Physics, volume 3
Essential chapters: Chapter 1-12 (besides chapter 4 which is optional)
I strongly recommend getting "Exercises for the Feynman Lectures on Physics" as well, and doing the problems. It's available online for fairly cheap (less than $20 USD).
Introduction to Linear Algebra by Gilbert Strang
(NOT Applications of Linear Algebra by Gilbert Strang)
Essential chapters: my recommendation here depends on your background. If you're familiar with linear algebra but you need some brushing up, or you've watched my videos, I'd recommend the following order:
Chapter 1 Introduction to Vectors + Chapter 3.1 Spaces of Vectors (https://youtu.be/3ZfrJ0Sk5iY)
Chapter 8 Linear Transformations (https://youtu.be/CBIO4xJ1Cok and https://youtu.be/ESKcF8XFzLM)
Chapter 6 Eigenvalues and Eigenvectors
Chapter 9 Complex Vectors and Matrices
If you're unfamiliar with linear algebra, I'd recommend doing a lot more of the introductory chapters, like chapter 2 as well as the above, and doing them in the order they appear in the text. It might also help to get some general intuition for Linear Algebra, for example from 3Blue1Brown's linear algebra videos (but make sure you do problem sets too!): https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab
Solutions to the problem sets: http://math.mit.edu/~gs/linearalgebra/
Video lectures by the author: https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/ The videos don't cover everything you need, and they don't come with problem sheets- though they do have past exams.
This book have at least 5 editions, and the ones I've checked seem to cover the above material so get a second hand copy of any of them.
Quantum Mechanics: The Theoretical Minimum by Leonard Susskind and Art Friedman (note, there are other 'theoretical minimum' books)
This book is priced like a novel (at least the penguin paperback version is) and, at least in Europe, seems to be widely available in book stores. The lectures this book is based on are here: https://www.youtube.com/playlist?list=PL701CD168D02FF56F
The big draw back of this book is that it doesn't have problem sets. I don't think it's easy to absorb this material without them, so that's why I also recommend the following book.
A Modern Approach to Quantum Mechanics by Townsend
This book goes a bit further than you might need, so below are the essential chapters, along with how these chapters match up with those in The Theoretical Minimum
Chapter 1 (Chapter 1 TTM)
Chapter 2&3 (Chapter 2&3 TTM)
Chapter 4 (Chapter 4&5 TTM, but uncertainty stuff was partially covered in Chapter 3 of Townsend)
Chapter 5 (Chapter 6&7 TTM)
Chapter 6 (Chapter 7&8 TTM)
Chapter 7 (Chapter 10 TTM)
This book is not cheap new. You could try and find a secondhand copy. Otherwise, see if your local library has it or is willing to get it. Another thing that might work is that many universities allow visitors to use books (but not borrow them). (There's also the option of searching for 'the book's name + pdf' if you want to do that, but I'm not necessarily endorsing it.)
Advanced topics!
This section is for after you've covered (a fair bit) of the above, or if you've learnt QM before. I'm much much less sure about these recommendations, because when it comes to advanced topics there's much more room for personal preference. Also, these books are more expensive and harder to find so I've given you some free links which you can read instead/before you get the book. Still, I'll give you some of my favourite ones.
Quantum Computing
The one classic text for this is by Nielsen and Chuang. However, if you just want an overview, you might be better off with lecture notes that are available online, for example Mermin's excellent notes: http://www.lassp.cornell.edu/mermin/qcomp/CS483.html
Quantum Complexity Theory
This is quantum computing for a computer science perspective. Scott Aaronson has a great book on it, based on these lecture notes: https://www.scottaaronson.com/democritus/
Quantum Foundations
Decoherence and the quantum to classical transition by Schlosshauer is a wonderful book that helps explain why the world seems classical when it's actually quantum. He makes an excellent case for the Many Worlds interpretation along the way. It does get quite technical though, and a lot of the value is toward the beginning. So I think this article by the author covers a lot of the most salient points: https://arxiv.org/pdf/quant-ph/0312059.pdf
Sneaking a look at God's cards by Ghirardi is one of my favourites and really put me onto foundations. It has an excellent discussion of the EPR paradox and hidden variables. Another good resource is Mermin's article on Bell's inequalities: https://cp3.irmp.ucl.ac.be/~maltoni/PHY1222/mermin_moon.pdf
Emergent multiverse is philosophy and physics legend David Wallace's defence of the Many Worlds interpretation of QM. A beautiful book, but it's dense in philosophy and physics so it's not a light read. Perhaps this will give the flavour of it: https://arxiv.org/pdf/quant-ph/0103092.pdf
Quantum Field Theory
An interpretive introduction to quantum field theory by Teller is nothing like any normal QFT textbook. Instead of all being mathematics, he spends a lot of time on what it means.
Quantum Chemistry/ computational chemistry
I've recently been reading about this because this is expected to be an area that quantum computing will really help with. I don't know anywhere near enough to recommend a textbook, but here's a nice review article: https://arxiv.org/pdf/1812.09976.pdf
I think it really helps to discuss problem sets with other people when you're stuck and to help explain things (kindly!) to others when they're confused, so here's a reddit where you can post your questions: https://old.reddit.com/r/Looking_glass_u/
Leave any comments either here or on the video about any concerns or corrections you have!