ALGEBRAIC NUMBERS AND ALGEBRAIC FUNCTIONS

Famous Norwegian mathematician Niels Henrik Abel advised that one should 'learn from the masters, not from the pupils'. When the subject is algebraic numbers and algebraic functions, there is no greater master than Emil Artin. In this classic text, originated from the notes of the course given at Princeton University in 1950-1951 and first published in 1967, one has a beautiful introduction to the subject accompanied by Artin's unique insights and perspectives. The exposition starts with the general theory of valuation fields in Part I, proceeds to the local class field theory in Part II, and then to the theory of function fields in one variable (including the Riemann-Roch theorem and its applications) in Part III.