/u/another_user_name posted this list a while back. Actual aerospace textbooks are towards the bottom but you'll need a working knowledge of the prereqs first.

Non-core/Pre-reqs:

Mathematics:

Calculus.

1-4) Calculus, Stewart -- This is a very common book and I felt it was ok, but there's mixed opinions about it. Try to get a cheap, used copy.

1-4) Calculus, A New Horizon, Anton -- This is highly valued by many people, but I haven't read it.

1-4) Essential Calculus With Applications, Silverman -- Dover book.

More discussion in this reddit thread.

Linear Algebra

3) Linear Algebra and Its Applications,Lay -- I had this one in school. I think it was decent.

3) Linear Algebra, Shilov -- Dover book.

Differential Equations

4) An Introduction to Ordinary Differential Equations, Coddington -- Dover book, highly reviewed on Amazon.

G) Partial Differential Equations, Evans

G) Partial Differential Equations For Scientists and Engineers, Farlow

More discussion here.

Numerical Analysis

5) Numerical Analysis, Burden and Faires

Chemistry:

1. General Chemistry, Pauling is a good, low cost choice. I'm not sure what we used in school.
   
   

   Physics:
   

   
   2-4) Physics, Cutnel -- This was highly recommended, but I've not read it.
   
   

   Programming:
   

   
   

   Introductory Programming
   

   
   Programming is becoming unavoidable as an engineering skill. I think Python is a strong introductory language that's got a lot of uses in industry.
   
   

2. Learning Python, Lutz
   
   
3. Learn Python the Hard Way, Shaw -- Gaining popularity, also free online.
   
   

   Core Curriculum:
   

   
   

   Introduction:
   

   
   

4. Introduction to Flight, Anderson
   
   

   Aerodynamics:
   

   
   

5. Introduction to Fluid Mechanics, Fox, Pritchard McDonald
   
   
6. Fundamentals of Aerodynamics, Anderson
   
   
7. Theory of Wing Sections, Abbot and von Doenhoff -- Dover book, but very good for what it is.
   
   
8. Aerodynamics for Engineers, Bertin and Cummings -- Didn't use this as the text (used Anderson instead) but it's got more on stuff like Vortex Lattice Methods.
   
   
9. Modern Compressible Flow: With Historical Perspective, Anderson
   
   
10. Computational Fluid Dynamics, Anderson
    
    

    Thermodynamics, Heat transfer and Propulsion:
    

    
    

11. Introduction to Thermodynamics and Heat Transfer, Cengel
    
    
12. Mechanics and Thermodynamics of Propulsion, Hill and Peterson
    
    

    Flight Mechanics, Stability and Control
    

    
    5+) Flight Stability and Automatic Control, Nelson
    
    5+)[Performance, Stability, Dynamics, and Control of Airplanes, Second Edition](http://www.amazon.com/Performance-Stability-Dynamics-Airplanes-Education/dp/1563475839/ref=sr_1_1?ie=UTF8&qid=1315534435&sr=8-1, Pamadi) -- I gather this is better than Nelson
    
    

13. Airplane Aerodynamics and Performance, Roskam and Lan
    
    

    Engineering Mechanics and Structures:
    

    
    3-4) Engineering Mechanics: Statics and Dynamics, Hibbeler
    
    

14. Mechanics of Materials, Hibbeler
    
    
15. Mechanical Vibrations, Rao
    
    
16. Practical Stress Analysis for Design Engineers: Design & Analysis of Aerospace Vehicle Structures, Flabel
    
    6-8) Analysis and Design of Flight Vehicle Structures, Bruhn -- A good reference, never really used it as a text.
    
    
17. An Introduction to the Finite Element Method, Reddy
    
    G) Introduction to the Mechanics of a Continuous Medium, Malvern
    
    G) Fracture Mechanics, Anderson
    
    G) Mechanics of Composite Materials, Jones
    
    

    Electrical Engineering
    

    
    

18. Electrical Engineering Principles and Applications, Hambley
    
    

    Design and Optimization
    

    
    

19. Fundamentals of Aircraft and Airship Design, Nicolai and Carinchner
    
    
20. Aircraft Design: A Conceptual Approach, Raymer
    
    
21. Engineering Optimization: Theory and Practice, Rao
    
    

    Space Systems
    

    
    

22. Fundamentals of Astrodynamics and Applications, Vallado
    
    
23. Introduction to Space Dynamics, Thomson -- Dover book
    
    
24. Orbital Mechanics, Prussing and Conway
    
    
25. Fundamentals of Astrodynamics, Bate, Mueller and White
    
    
26. Space Mission Analysis and Design, Wertz and Larson

Just buy a Calculus textbook and watch all of the videos on PatrickJMT/KhanAcademy.

I took the calculus sequence at a University, but 90% of what I learned was from the book and online resources.

The most popular calculus book for college classes in the United States is Stewart, Calculus: Early Transcendentals. A typical Calculus II course starts somewhere in chapter 5 or 6 (picking up wherever Calculus I left off) and ends with chapter 11.

This book has answers to all of the odd-numbered exercises in the back, so it works reasonably well to read the book and then try the exercises. Typically the first 3/4 of the exercises in each section are straightforward, and the remaining 1/4 are more difficult and would only be assigned in an honors class.

I'm a student (Junior ME) so my recommendation would be better suited over at /r/engineeringstudents but if you wanted to get started on the entry level coursework. Here's where you can start.

Calculus

http://www.amazon.com/Calculus-Early-Transcendentals-Stewarts-Series/dp/0495011665/ref=sr_1_2?ie=UTF8&qid=1371011569&sr=8-2&keywords=stewart+calculus+6th+edition

Physics

http://www.amazon.com/Physics-Scientists-Engineers-Strategic-Approach/dp/0321516591/ref=sr_1_2?s=books&ie=UTF8&qid=1371011593&sr=1-2&keywords=knight+physics+for+scientists+and+engineers+2nd+edition

Engineering Statics / Dynamics

http://www.amazon.com/Engineering-Mechanics-Combined-Statics-Dynamics/dp/0138149291/ref=sr_1_9?s=books&ie=UTF8&qid=1371011626&sr=1-9&keywords=hibbler+statics+dynamics

Engineering Mechanics of Materials

http://www.amazon.com/Mechanics-Materials-8th-Russell-Hibbeler/dp/0136022308/ref=sr_1_1?s=books&ie=UTF8&qid=1371011680&sr=1-1&keywords=hibbler+mechanics+of+materials

For a very good textbook, I would recommend Calculus Early transcendentals by Stewart. He goes through every concept in single variable calculus (there's also a version with multi variable calculus) and proves almost every concept he teaches. Its one of my favorite textbooks in general.

I'd recommend hitting up somewhere like half-price books and grabbing a textbook for like $10-$15. I purchased this book for probably $12 when I needed to brush up. I know it's not online, but it will provide good direction, offer a solid foundation, provide sample problems to test your knowledge, and can easily be supplemented by online materials. As someone else mentioned, Khan Academy is also great, but I would highly recommend using them as a supplement, and using a book as your base.

Game Engine:

Game Engine Architecture by Jason Gregory, best you can get.

Game Coding Complete by Mike McShaffry. The book goes over the whole of making a game from start to finish, so it's a great way to learn the interaction the engine has with the gameplay code. Though, I admit I also am not a particular fan of his coding style, but have found ways around it. The boost library adds some complexity that makes the code more terse. The 4th edition made a point of not using it after many met with some difficulty with it in the 3rd edition. The book also uses DXUT to abstract the DirectX functionality necessary to render things on screen. Although that is one approach, I found that getting DXUT set up properly can be somewhat of a pain, and the abstraction hides really interesting details about the whole task of 3D rendering. You have a strong background in graphics, so you will probably be better served by more direct access to the DirectX API calls. This leads into my suggestion for Introduction to 3D Game Programming with DirectX10 (or DirectX11).



C++:

C++ Pocket Reference by Kyle Loudon
I remember reading that it takes years if not decades to become a master at C++. You have a lot of C++ experience, so you might be better served by a small reference book than a large textbook. I like having this around to reference the features that I use less often. Example:

namespace
{
//code here
}

is an unnamed namespace, which is a preferred method for declaring functions or variables with file scope. You don't see this too often in sample textbook code, but it will crop up from time to time in samples from other programmers on the web. It's $10 or so, and I find it faster and handier than standard online documentation.



Math:

You have a solid graphics background, but just in case you need good references for math:
3D Math Primer
Mathematics for 3D Game Programming

Also, really advanced lighting techniques stretch into the field of Multivariate Calculus. Calculus: Early Transcendentals Chapters >= 11 fall in that field.



Rendering:

Introduction to 3D Game Programming with DirectX10 by Frank. D. Luna.
You should probably get the DirectX11 version when it is available, not because it's newer, not because DirectX10 is obsolete (it's not yet), but because the new DirectX11 book has a chapter on animation. The directX 10 book sorely lacks it. But your solid graphics background may make this obsolete for you.

3D Game Engine Architecture (with Wild Magic) by David H. Eberly is a good book with a lot of parallels to Game Engine Architecture, but focuses much more on the 3D rendering portion of the engine, so you get a better depth of knowledge for rendering in the context of a game engine. I haven't had a chance to read much of this one, so I can't be sure of how useful it is just yet. I also haven't had the pleasure of obtaining its sister book 3D Game Engine Design.

Given your strong graphics background, you will probably want to go past the basics and get to the really nifty stuff. Real-Time Rendering, Third Edition by Tomas Akenine-Moller, Eric Haines, Naty Hoffman is a good book of the more advanced techniques, so you might look there for material to push your graphics knowledge boundaries.



Software Engineering:

I don't have a good book to suggest for this topic, so hopefully another redditor will follow up on this.

If you haven't already, be sure to read about software engineering. It teaches you how to design a process for development, the stages involved, effective methodologies for making and tracking progress, and all sorts of information on things that make programming and software development easier. Not all of it will be useful if you are a one man team, because software engineering is a discipline created around teams, but much of it still applies and will help you stay on track, know when you've been derailed, and help you make decisions that get you back on. Also, patterns. Patterns are great.

Note: I would not suggest Software Engineering for Game Developers. It's an ok book, but I've seen better, the structure doesn't seem to flow well (for me at least), and it seems to be missing some important topics, like user stories, Rational Unified Process, or Feature-Driven Development (I think Mojang does this, but I don't know for sure). Maybe those topics aren't very important for game development directly, but I've always found user stories to be useful.

Software Engineering in general will prove to be a useful field when you are developing your engine, and even more so if you have a team. Take a look at This article to get small taste of what Software Engineering is about.


Why so many books?
Game Engines are a collection of different systems and subsystems used in making games. Each system has its own background, perspective, concepts, and can be referred to from multiple angles. I like Game Engine Architecture's structure for showing an engine as a whole. Luna's DirectX10 book has a better Timer class. The DirectX book also has better explanations of the low-level rendering processes than Coding Complete or Engine Architecture. Engine Architecture and Game Coding Complete touch on Software Engineering, but not in great depth, which is important for team development. So I find that Game Coding Complete and Game Engine Architecture are your go to books, but in some cases only provide a surface layer understanding of some system, which isn't enough to implement your own engine on. The other books are listed here because I feel they provide a valuable supplement and more in depth explanations that will be useful when developing your engine.

tldr: What Valken and SpooderW said.

On the topic of XNA, anyone know a good XNA book? I have XNA Unleashed 3.0, but it's somewhat out of date to the new XNA 4.0. The best looking up-to-date one seems to be Learning XNA 4.0: Game Development for the PC, Xbox 360, and Windows Phone 7 . I have the 3.0 version of this book, and it's well done.

*****
Source: Doing an Independent Study in Game Engine Development. I asked this same question months ago, did my research, got most of the books listed here, and omitted ones that didn't have much usefulness. Thought I would share my research, hope you find it useful.

i can back this assessment up, as i used this text for the exact same thing. http://www.amazon.com/Calculus-Early-Transcendentals-Stewarts-Series/dp/0495011665 a broad text, well explained, with many helpful practice problems.

Barron's for gov and Calc ab. I would say James Stewart for calculus. Amazon should have his Calc book for cheap price https://www.amazon.com/Calculus-Early-Transcendentals-James-Stewart/dp/0495011665/ just read the chapters and do the problems. Khan academy is useful.

Awesome, I will take a look at that. Here is the book I have to teach myself with (used it for Calculus 2 a year ago). It seems like a solid book.

College books are also much more expensive in the USA than in Europe.

For example:

$152.71
VS
£43.62($68.03)

$146.26 VS
£44.34($69.16)