Introduction to basic number theory, including modern applications. Topics include: modular arithmetic; the Chinese remainder theorem, Fermat's little theorem, and Wilson's theorem; number-theoretic functions such as the τ, σ, Euler's φ-function; the Möbius inversion formula; applications to cryptography; primitive roots and indices; Legendre's symbols; the quadratic reciprocity law; continued fractions and Pell's equations; primality tests, factorization of integers, and the RSA cryptosystem.