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This book provides a concise and effective introduction to twisted Rabinowitz–Floer homology, a generalization of Rabinowitz–Floer homology. The theory can be used for finding periodic orbits in Hamiltonian systems: applications include results in celestial mechanics and space mission design. Written in a style that encourages active reflection and trains problem-solving abilities, the book offers a pathway for aspiring researchers from classical mechanics formulated in the language of symplectic geometry to current research in Rabinowitz–Floer homology and neighboring areas. The book features plenty of examples and exercises, including solutions to most of them, as well as open questions and further directions for research.