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Books to increase and solidify my knowledge

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I would like your opinions on what would be the best 3 books to buy.

I need a book that focuses entirely on DirectX, techniques like normal mapping, bump mapping etc and most importantly HLSL and shader programming.

I need a maths book on 3d game programming that gives you in-depth knowledge of what's happening when you do techniques like, I don't know, ray tracing, mesh intersection tests, all the basics and some advanced topics if possible.(While I'm not an idiot, please no books with equations in replacement of explanations)

And finally I want a book that will teach me to design well formatted game engines (My current engine is a mess :A)

I'm not really concerned about price btw =]
Cheers.

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I would think Frank Luna's Introduction to 3D Game Programming With DirectX 9.0c A Shader Approach is a good candidate for your first category.

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Yes, I would second that. Frank Luna has written some excellent stuff on this topic. I have one of his earlier books which touched upon shaders towards the end, and the bulk of that book proved to be invaluable in my transition from DX7 to DX9. Had some pretty good introductory chapters on 3D maths too.

However, if you want a serious mathematics book for 3D games and graphics, then may I recommend:

Mathematics for 3D Game Programming & Computer Graphics - By Eric Lengyel

This book has vast scope, from the very basics to the insane! And I like the highly logical explanations in it. Mathematics is a "pure" subject that is best explained using straight forward, concise and simple points, backed up with proof only when necessary.

Eric does this with ease and, to help solidify the concepts, each chapter set's you relevant questions, supplied with answers at the back of the book, plus coding exercises too. If you’re OK with Maths, then you should have no problems with this book.

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