This book, "Symplectic Invariants and Hamiltonian Dynamics" by Helmut Hofer and Eduard Zehnder, is a comprehensive treatment of symplectic invariants and their applications in Hamiltonian dynamics. The authors introduce and develop the concept of symplectic capacities, which are key tools for understanding the rigidity and dynamics of symplectic mappings. The book covers a wide range of topics, including: 1. **Introduction**: Basic concepts of symplectic vector spaces, diffeomorphisms, and Hamiltonian vector fields. 2. **Symplectic Capacities**: Definitions, properties, and applications to embeddings and rigidity phenomena. 3. **Existence of a Capacity**: Construction and properties of the distinguished capacity \( c_0 \). 4. **Existence of Closed Characteristics**: Analysis of periodic solutions on energy surfaces and hypersurfaces of contact type. 5. **Compactly Supported Symplectic Mappings**: Study of the Hofer metric and its relation to other symplectic invariants. 6. **Fixed Points and Geodesics**: Fixed point theory for Hamiltonian mappings and the Arnold conjecture. 7. **Floer Homology and Symplectic Homology**: Advanced topics including Floer's approach to Morse theory and symplectic homology. The book is structured to provide a detailed and systematic introduction to the field, making it accessible to readers with a background in mathematics and physics. It includes numerous examples, illustrations, and proofs, and is dedicated to the memory of Andreas Floer, a significant contributor to the field. The authors acknowledge the contributions of several colleagues and participants who provided valuable feedback and support during the writing process.This book, "Symplectic Invariants and Hamiltonian Dynamics" by Helmut Hofer and Eduard Zehnder, is a comprehensive treatment of symplectic invariants and their applications in Hamiltonian dynamics. The authors introduce and develop the concept of symplectic capacities, which are key tools for understanding the rigidity and dynamics of symplectic mappings. The book covers a wide range of topics, including: 1. **Introduction**: Basic concepts of symplectic vector spaces, diffeomorphisms, and Hamiltonian vector fields. 2. **Symplectic Capacities**: Definitions, properties, and applications to embeddings and rigidity phenomena. 3. **Existence of a Capacity**: Construction and properties of the distinguished capacity \( c_0 \). 4. **Existence of Closed Characteristics**: Analysis of periodic solutions on energy surfaces and hypersurfaces of contact type. 5. **Compactly Supported Symplectic Mappings**: Study of the Hofer metric and its relation to other symplectic invariants. 6. **Fixed Points and Geodesics**: Fixed point theory for Hamiltonian mappings and the Arnold conjecture. 7. **Floer Homology and Symplectic Homology**: Advanced topics including Floer's approach to Morse theory and symplectic homology. The book is structured to provide a detailed and systematic introduction to the field, making it accessible to readers with a background in mathematics and physics. It includes numerous examples, illustrations, and proofs, and is dedicated to the memory of Andreas Floer, a significant contributor to the field. The authors acknowledge the contributions of several colleagues and participants who provided valuable feedback and support during the writing process.