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: 
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
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.