What are some classic books in mathematics? In his book "Men of Mathematics", Eric Temple Bell repeatedly makes the point that a student of mathematics must read the classics.
My question is what are some classic books in mathematics ( Dictionary definition : judged over a period of time to be of the highest quality and outstanding of its kind.) that can be used by a high school/undergraduate student to start the study of higher mathematics? 
Some subjects I would like reference in particular, otherwise state any book you consider a classic, are:
1) Analysis
 2) Abstract algebra
 3) Linear Algebra
 4) Number theory
5) Combinatorics and Graph theory, etc.
 A: I don’t agree with Bell on this point: one may well learn better and more easily from a book that is not generally considered a classic. For example, most people have never even heard of John Greever’s modified Moore method textbook Theory and Examples of Point-Set Topology, but for me it was the ideal introduction to the field. That said, I can nevertheless name a few examples.
For someone of my generation I.N. Herstein’s Topics in Algebra is a classic introduction to abstract algebra. The first volume of William J. LeVeque’s two-volume Topics in Number Theory is a classic at the higher end of the undergraduate level; Underwood Dudley’s Elementary Number Theory is a classic at the lower end.
A: *

*Feller's first volume for Probability Theory.

*Arnold's ODE for differential equations.

*Cartan's Elementary Theory of Analytic Functions of One or Several Complex Variables for Complex Analysis

A: It's a bit more advanced than the topics you asked about, but Milnor's Morse Theory and Milnor and Stasheff's Characteristic Classes are astoundingly good. (There's a pattern here: Milnor's Lectures on the h-Cobordism Theorem is pretty good too!)
At a somewhat lower level, I find Spivak's Calculus (which many might argue is an introductory analysis book) pretty darned wonderful. 
A: The Mathematical Association of America (MAA) has got a rich collection of classic books under Doclani Mathematical Expositions. I would suggest you following:
$1$. Mathematical Gems Series ($3$ Volumes) By Ross Honsburger.
$2$. Linear Algebra problem book By Paul R Halmos.
$3$. Euler: Master of us all By William Dunham.
Some other texts:
$1$ Introduction to Commutative Algebra by Atiyah and MacDonald.
$2$ A book of abstract algebra by Pinter.
A: In the early '70s, I used two teaching books that I consider ''classic'':
Foundations of modern analysis of J. Dieudonné (at least in Europe).
Algebra  of S. Mac Lane and G. Birkoff
At a different level, I think that an ''evergreen'' is:
Methods of Mathematical physics of R. Courant and D. Hilbert.
