Question: 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.

Answer: 
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.
1. Feller's first volume for Probability Theory.
2. Arnold's ODE for differential equations.
3. Cartan's Elementary Theory of Analytic Functions of One or Several Complex Variables for Complex Analysis