Studies the robust analogies between number theory of the integers and of function fields in one variable over a finite field. Elementary topics include unique factorization, the prime number theorem, Dirichlet's theorem on primes in arithmetic progression, and the power reciprocity law. Additional topics include algebraic function fields, valuations, divisors, differentials, the Riemann-Roch theorem and its applications, zeta functions, Galois theory of function fields, the Weil conjectures, and the Riemann hypothesis for curves.