Cryptography studies how to perform computational tasks securely in adversarial environments. It plays an important role in designing secure systems. This is an introductory course that covers basic concepts and proof techniques in this area, as well as some recent research trends. The course is theoretical in nature, with emphasis on proofs and algorithmic reductions, even when discussing applied topics. No prior background in cryptography is assumed. However, students should have mathematical maturity and be comfortable with definitions and proofs.