Book excerpt: This book is intended as a teacher's manual and a self-study handbook for high-school or college students, and mathematical competitors. It consists mainly of problems created by the authors, with author-prepared-solutions, which were used in different national and international Mathematical Olympiads from 1984 to 2019. The book is arranged by topic and difficulty level. The book gives a broad view of mathematics and goes well beyond the elementary mathematics by providing deeper treatments of the following topics: Geometry and Trigonometry, Number theory, Algebra, Combinatorics and Calculus.