Solving mathematical problmes is a favourite pastime of many people, from school students to professional research mathematicians. The aim of this book is to provide a wide variety of problems suitable for teenagers and students which will stimulate interest in mathematical ideas and methods outside the usual school syllabus. The problems vary in their difficulty, but are all intended to encourage independent investigation, to demonstrate different approaches to problem-solving, and to illustrate some of the famous problems that famous mathematicians have attempted to solve. For each problem the author has provided hints and a detailed discussion of their solution. Consequently, the book will provide a valuable teaching resource for schools, teacher training, and university mathematics courses. The problems themselves range from the easy to the unsolved and will provide much enjoyment for all those fascinated by mathematical ideas.