List of Recommended Textbooks

[Layra-chan]

Books that have been recommended by someone for something:

Mathematics:
Calculus
Linear Algebra
Geometry
Abstract Algebra
Analysis
ODE/PDE

Physics:
Newtonian Mechanics
Special Relativity
General Relativity
Quantum Mechanics
QFT
Thermodynamics

Astronomy
I have no idea what the subfields are

Material Science
See Astronomy

Please recommend textbooks that you thought were clear, informative, comprehensive, etc. Textbooks that you think would be good reading material in a physics or mathematics class.
Note: I would rather not have popsci books, not just because I dislike the genre, but also because they, by their very nature, do not actually teach the details needed to get a solid, usable understanding of the material.  

[Dread and Freedom]

Calculus:

Spivak if you're feeling cheeky.

If you're just starting out, The "For Dummies" and "Demystified" books on calculus are actually very good jump off points. And I actually used them as primary texts instead of supplemental ones when I first taught myself.

ODE/PDE
Ordinary Differential Equations by Morris Tenenbaum and some other dude. It's cheap, and EXTREMELY comprehensive. It's a little dated, but it has oodles of problems and practical examples. As well as a surprisingly strong theoretical foundation.

Geometry:

Spivak did Differential Geometry too. It's good stuff.

Analysis:

Rudin, duuuuh.

Abstract Algebra:
Gallian (obv)
Dummit Foote (Obv but not for new comers)

Other:

Fractal Geometry - Mathematical Foundations and Applications , John Wiley, Second Edition, 2003

Seriously, it's a wonderful book.  

[Mecill]

What level is Spivak Calculus at? I am interested in finding a calculus book at a more advanced level.

The one I have currently is Varberg, Purcell, Rigdon. (It is quite interesting to read but not very good as a problem solving reference.) I believe the book I used for Calc I and II was Finney, Demana, Waits, Kennedy which I no longer have a copy of it, but had no problems with (until I got to series) when I first learned Calc. The other book I have seen used for undergrads is Thomas.

For self-study of classical mechanics I have Taylor.

A book recommended by Griffiths, (the author of the commonly used undergrad E&M book) is Mathematical Methods for the Physical Sciences by Boas. I used it a few times and liked it. Now I have Arfken & Weber's Mathematical Methods for Physicists which seems more serious. ^_^

For starting Quantum Mechanics I like Quantum Physics by Gasiorowicz.  

[Mecill]

For Astronomy, here is a book on the interstellar medium: http://books.google.com/books?id=IoO7a6G8gJYC&lpg=PP1&lr=&pg=PP1#v=onepage&q=&f=false

Also, a book I would like to recommend which can be read by both laypeople and scientists is Surely You're Joking, Mr. Feynman. I would like to warn you that it sounds like Feynman was kind of an irresponsible guy who was very smart and maybe a little lucky. But it is a fun read, especially if you know some physics. Do not use it like a text book! Read it like a novel.  

[Miscenco]

Some books that I've been reccommended many times in the past year for Physics and Maths are:
Introduction to Electrodynamics, and Introduction to Quantum Mechanics, both by D.J. Griffiths.
Mathematical Methods in the Physical Sciences, by M. Boas.
They are at University level, so... yeah. I found/am finding them to be very helpful for the second year of my degree. They can be a little dry, but they are good books.
They both tend to delve right in to the science and leaves out a little back-information.

Oh, I know that this is a bit popsci, but I've been advised to read some of the technical manuals for Star Trek. Surprisingly, they have some good science in them. XD