An introduction to basic counting techniques for upper secondary and junior college students, as well as teachers. Younger students and lay people who appreciate mathematics or puzzle solving, should also find the book interesting. The various problems and applications here should help build up proficiency in counting, and hone basic skills and techniques in general problem solving. Many of the problems avoid routine and the diligent reader will often discover more than one way of solving a particular problem, which is an important awareness in problem solving. The book is thus designed to give students an early start to learning problem-solving heuristics and thinking skills.