Includes bibliographical references (p. [341]-351) and index.

Machine generated contents note: 1 Polynomials over Finite Fields 1 -- Exercises7 -- 2 Primes, Arithmetic Functions, and the Zeta Function 11 -- Exercises19 -- 3 The Reciprocity Law 23 -- Exercises30 -- 4 Diril'et L-Series and Primes in an Arithmetic Progression 33 -- Exercises43 -- 5 Algebraic Function Fields and Global Function Fields 45 -- Exercises59 -- 6 Weil Differentials and the Canonical Class 63 -- Exercises75 -- 7 Extensions of Function Fields, Riemann-Hurwitz, -- and the ABC Theorem 77 -- Exercises98 -- 8 Constant Field Extensions 101 -- Exercises112 -- 9 Galois Extensions - Hecke and Artin L-Series 115 -- Exercises145 -- 10 Artin's Primitive Root Conjecture 149 -- Exercises166 -- 11 The Behavior of the Class Group in Constant Field Extensions 169 -- Exercises190 -- 12 Cyclotomic Function Fields 193 -- Exercises216 -- 13 Drinfeld Modules: An Introduction 219 -- Exercises239 -- 14 S-Units, S-Class Group, and the Corresponding L-Functions 241 -- Exercises256 -- 15 The Brumer-Stark Conjecture 257 -- Exercises278 -- 16 The Class Number Formulas in Quadratic -- and Cyclotomic Function Fields 283 -- Exercises302 -- 17 Average Value Theorems in Function Fields 305 -- Exercises326 -- Appendix: A Proof of the Function Field Riemann Hypothesis 329 -- Bibliography 341 -- Author Index 353 -- Subject Index 355.