Here is a collection of unusual problems and puzzles which are designed to help students develop their capacity to think through difficult mathematical problems in an enjoyable and challenging way. The problems are grouped into 29 sections, each developing a single theme, with each section followed by a commentary suggesting ideas and approaches that students can try. Advanced math is not required, and most sections are accessible to younger students. The emphasis is on intuitive and investigative approaches which can stimulate individual creativity and provide a focus for group discussion and learning.