This carefully developed problem book takes a unique, intuitive approach to extreme value problems, treating them within the framework of Euclidean geometry. Included is a comprehensive selection of maxima and minima problems, from classical Greek constructions to modern, recently solved problems; detailed, step-by-step solutions to many of the exercises are provided. The reader is exposed to algebra, analysis, combinatorics, and topology, and throughout the text, emphasis is placed on creative techniques for problem solving. Reflecting the authors’ experience as professors and Olympiad coaches, this volume is ideal for use at the junior and senior undergraduate level, as well as for enrichment programs and Olympiad training for advanced high school students. The book will also appeal to graduate students, professional mathematicians, and puzzle enthusiasts alike.