The Hill cipher is the simplest example of a "block cipher," which takes a block of plaintext as input, and returns a block of ciphertext as output. Although it is insecure by modern standards, its simplicity means that it is well suited for the teaching of such concepts as encryption modes, and properties of cryptographic hash functions. Although these topics are central to modern cryptography, it is hard to find good simple examples of their use. The conceptual and computational simplicity of the Hill cipher means that students can experiment with these topics, see them in action, and obtain a better understanding that would be possible from a theoretical discussion alone. In this article, we define the Hill cipher and demonstrate its use with different modes of encryption, and also show how cryptographic hash functions can be both designed and broken. Finally, we look at some pedagogical considerations. (Contains 2 figures.)