This book was designed to accompany a mathematics course bearing the same name (Math 157, Spring 2015, Harvard). The idea behind the class has been to teach problem solving skills to a wide audience. Each lecture is organized around a number of problems which we interleave with the more general discussion of useful principles and ideas. Student participation and interaction and not only encouraged, but often required.

We decided to publish a list of problems that came up as part of the course. Please note that this text is very much a work in progress. We welcome all contributions, from new problems and alternative solutions, to clarifications and spelling corrections.