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.
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.