This chapter studies the theorems of Fermat, Euler , and Lagrange . Fermat's theorem states that if p is prime, then n^p-n is a multiple of p for every n. This is the basic tool in the arithmetic of congruences. Euler generalized Fermat's theroem to composite moduli by introducing the phi-function. Lagrange's theorem gives an upper bound on the number of solutions to higher degree congruences modulo primes.