This book describes mini-courses in a Mathematical "Circle," i.e., an organization that discovers and nurtures young mathematical talents through meaningful extra-curricular activities. This is the third volume in a trilogy describing in particular the S.M.A.R.T. Circle project, which was founded in Edmonton, Canada in 1981. The acronym S.M.A.R.T. stands for Saturday Mathematical Activities, Recreations & Tutorials. This book, Volume III, consists of mini-courses and explains what actually takes place in the Circle. Volume I describes how to run a Circle, and Volume II, consisting of student projects, addresses the purpose of the Circle. All three volumes provide a wealth of resources (mathematical problems, quizzes and games, together with their solutions). The books will be of interest to self-motivated students who want to conduct independent research, teachers who work with these students, and teachers who are currently running or planning to run Mathematical Circles of their own.