This course deals with the study of modern cryptography from a theoretical perspective, the emphasis of the course being on "provable security". In particular, we study the cryptographic primitives that are the building-blocks of various cryptographic applications. The course involves the study of notions of security for a given cryptographic primitive, its various constructions, and respective security analysis based on the security notion. The cryptographic primitives that we cover include pseudorandom functions, symmetric encryption (block ciphers), hash functions and random oracles, message authentication code, asymmetric encryption and digital signatures. Time permitting; we also study how to build secure cryptographic protocols for authenticated key exchange, using the primitives that we study. We also study various number-theoretic assumptions cryptography is based upon.