SOME TOPICS IN ELEMENTARY NUMBER THEORY: Time estimates for doing arithmetic. Divisibility and the Euclidean algorithm. Congruences. Some applications to factoring; FINITE FIELDS AND QUADRATIC RESIDUES: Finite fields. Quadratic residues and reciprocity; CRYPTOGRAPHY: some simple cryptosystems. Enciphering matrices; PUBLIC KEY: The idea of public-key cryptography. RSA. Discrete log; ELLIPTIC CURVES: Basic facts. Elliptic curve cryptosystems.