Cryptography is an indispensable tool for protecting information in computer systems. This course explains the inner workings of cryptographic primitives and how to correctly use them. Students will learn how to reason about the security of cryptographic constructions and how to apply this knowledge to real-world applications. The course begins with a detailed discussion of how two parties who have a shared secret key can communicate securely when a powerful adversary eavesdrops and tampers with traffic. We will examine many deployed protocols and analyze mistakes in existing systems. The second half of the course discusses public-key techniques that let two or more parties generate a shared secret key. We will cover the relevant number theory and discuss public-key encryption, digital signatures, and authentication protocols. Towards the end of the course we will cover more advanced topics such as zero-knowledge, privacy mechanisms, and other forms of encryption. Throughout the course students will be exposed to many exciting open problems in the field.