One of the main purposes of a mathematics club is to provide the opportunity for students to study exciting topics in mathematics not ordinarily discussed in the classroom. Each of the 10 chapters in this booklet is a collection of related subtopics. Each idea is presented and discussed; bibliographies then suggest in-depth reading. The chapters focus on: Fibonacci sequences, projective geometry, groups, infinity and transfinite numbers, Pascal's triangle, topology, experiments with natural numbers, non-Euclidean geometries, computers, and how close is close. (MNS)