ho.history overview - Map of Number Theory

Your question about one book for number theory is like a non-mathematician asking about one book for all mathematics. It is simply not possible. It is a growing subject in various directions. The best I can attempt is to give a book each for each direction, approximating your question. It is impossible to give anything better than this.

For Analytic Number Theory, what you ask can be achieved by:

Iwaniec And Kowalski, Analytic Number Theory.

This is THE book. It is quite comprehensive. Includes L-functions, modular forms, random matrices, whatever.

For algebraic number theory, the book:

Cassels and Frohlich, Algebraic Number Theory

would tell you all about developments upto Classfield Theory and Tate's thesis. Includes the cohomological version. This is a MUST for algebraic number theorists.

For Langlands' program, use the reference that Pete gives.

For Iwasawa theory, there are two books by Coates and Sujatha.

You might want to know a bit more about the applications of algebraic geometry into number theory. The way to go is through Silverman on elliptic curves, Q. Liu's book, Serre's books, etc..

A historic overview up to the time of Legendre can be found in Weil's book, "Number theory through history: From Hammurapi to Legendre".