As early as the time of Julius Caesar, people have tried to communicate secretly with others. Today we use passwords and PINs to authenticate who we say we are and to link our actions to our identity. We purchase products online, never thinking twice about entering our credit card number – a direct link to our money – into a web browser. We do this comfortably because of high-powered mathematics. Cryptology is the area of mathematics that studies cryptography, the art of encrypting messages, and crypt-analysis, the science of breaking encrypted messages. This first-year seminar studies these ideas broadly through mathematical explorations accessible to the inquisitive student with only basic algebra skills. Modular arithmetic, greatest common divisors, and large prime numbers play a supporting role in our course, but learning to research, write, and speak effectively, both individually and in a team, are the featured acts. We look at how to encrypt text and images, and we exchange our encrypted messages, challenging our classmates to break our ciphers. Major advances in cryptology throughout history will also be explored, from the early times of Caesar and Vigenère to the more recent discoveries of public key ciphers used in modern electronic commerce. In the end, you will have gained insights into the deep mathematical and statistical ideas that drive the implementation and analysis of modern cryptological techniques, as well as the nuances and pitfalls of creating secure encryption systems.