This presentation of systematic methods for winning differential games of pursuit and evasion explores the procedures' scope and applications. Numerous helpful examples illustrate basic and advanced concepts, including capture, strategy, and algebraic theory.Author Otomar Hájek, Professor Emeritus of Mathematics at Case Western Reserve University, designed this text for advanced undergraduate and graduate courses in applied mathematics and systems engineering. The opening chapters focus on examples, applications, and basic concepts, advancing to considerations of linear and nonlinear games. Topics include stroboscopic and isochronous capture, algebraic theory, and strategies. Detailed proofs appear throughout the text, along with 200 exercises that further clarify each subject.