This book compiles thoughtfully curated selection tests proposed to IMO (International Mathematical Olympiad) teams across many countries. Offering a blend of original solutions and adaptations by the author, this work is chronologically organized, featuring problems from 1968 to 2024, and provides a unique insight into the evolution of this mathematical contest. The work starts with a section containing key theories and examples, serving as a quick reference guide. The main inequalities and functional equations are covered, along with topics on mathematical induction and polynomials. This is followed by the problems themselves, covering equations and systems of equations, inequalities, functional equations and inequalities, mathematical induction, and polynomials. A meticulously crafted index helps the reader navigate through the topics with ease. References are provided for further reading and self-study. Besides serving as an invaluable preparation tool for both aspiring students and those passionate about mathematics alike, this book also complements Selection Tests in Number Theory for Mathematical Olympiads, from the same author, available at Springer.