This book is a buffet of mathematical methods for problem solving. It contains a large collection of problems that have been carefully selected and organized in a way to help preparing for olympiad level competitions. The book also contains a thorough description of the tools and techniques that can be used to solve these problems. Special emphasis is put on describing how to think and solve problems like a professional mathematician, giving plenty of hands-on advice that has shown to be effective.The book is primarily written for students involved in highschool level mathematical competitions, on national as well as international level, but could also be of interest to highschool teachers and university students with an interest in mathematical problem solving.