I saw a lot of books which cover specific topics, but is there a book or a recommendation of a few books which covers the basic of everything involved in making a game? I know this would only cover the basics, but that would be a good starting point to later read more into specific topics.
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The Art of Game Design: A Book of Lenses - as making games isn't only about programming.
start with flash, there are plenty of resourcces and some really good books:
http://www.emanueleferonato.com - some good beginner code but the structure and efficency of the code is sometimes bad, but its a good and fast start
also this will probably have better code http://www.amazon.com/ActionScript-3-0-Game-Programming-University/dp/0789747324/ref=sr_1_1?ie=UTF8&qid=1302401359&sr=8-1
I skimmed it, it was fairly basic but an excellent start.
http://www.lynda.com/ActionScript-3-tutorials/projects-game-development/366-2.html a video guide into game development. It depends on your style of learning, if you like just looking at a source code and using that as a starting point, I would recommend the books, but if you're new to programming the video tutorial guide will be great help for you.
finally after getting all that done you'll have a good understanding of object oriented programming, after which you should read: http://www.amazon.ca/ActionScript-3-0-Design-Patterns-Programming/dp/0596528469
Design Patters will help you effectively create bigger games, and allow you to better transfer your skills to other languages. Don't need to read everything but make sure you read the chapters on inheritance, polymorphism, factory design patterns, and model view component.
However, you decide to learn make sure you actually program the code and not just read or watch it. Pick a sample game you want to learn every 2 weeks and really try to understand the code, where you don't have to reference the book too much - if you get stuck don't look at the ans in the book but try and googleing it, being a good googler and understanding how to read the documents for you language is really helpful. If you do those within maybe the next 5-10 months you should be able to make those games within 2 days (the logic at least) - but at that point you should move the the next plateau
I would then recommend moving onto C# creating games on XNA for xbox live and windows 7. Its a very good game development platform, and will be some good books on it in the next few months (xna just got updated so a lot of material online is still outdated), C# is a lot like as3 so don't spend too much time on it, just get comfortable with the language make a few games then move on.
I would say make a java game next for android, but if you think you're ready learn some C++. But before moving to C++ read: http://www.amazon.com/Data-Structures-Algorithms-Developers-Development/dp/1584504951/ref=sr_1_2?s=books&ie=UTF8&qid=1301897090&sr=1-2 get a good familiarity with algorithms and data structures.
P.S game programming and programming in general are frustrating so don't be demotivated every must go through that battlefield; if you find yourself really feeling comfortable and able to make games/app without much problem you need to move to harder material, because its a trap!
If you're about C++ game development then..
Steve Rabin's Introduction to Game Development 2nd Edition.
Mike McShaffrey's Game Coding Complete 3rd Edition.
Gregory and Lander's Game Engine Architecture.
If you just want an overview of general game development (non C++ specific) then might be better to look elsewhere...