This overview of symplectic geometry, written for the *Handbook of Differential Geometry*, covers the following topics: 1. **Symplectic Manifolds**: These are manifolds equipped with a symplectic form, a closed nondegenerate 2-form. Symplectic manifolds are necessarily even-dimensional and orientable. The chapter discusses basic properties, classical examples, equivalence notions, local normal forms, and symplectic submanifolds. 2. **Lagrangian Submanifolds**: These are submanifolds of symplectic manifolds of half dimension where the restriction of the symplectic form vanishes identically. The chapter describes normal neighborhoods of Lagrangian submanifolds and their applications. 3. **Complex Structures**: Any symplectic manifold admits almost complex structures, and these structures are compatible with the symplectic form. The chapter includes the local normal form for Kähler manifolds and a summary of Hodge theory. 4. **Symplectic Geography**: This topic concerns the existence and uniqueness of symplectic forms on a given manifold. It includes constructions of symplectic manifolds and invariants to distinguish them. 5. **Hamiltonian Geometry**: This geometry is concerned with symplectic manifolds equipped with a moment map, which is a collection of quantities conserved by symmetries. The chapter discusses the geometry of moment maps, including the classical Legendre transform, integrable systems, and convexity. 6. **Symplectic Reduction**: This is a fundamental tool in symplectic arguments, with infinite-dimensional analogues that have significant consequences for differential geometry. The chapter covers the Marsden-Weinstein-Meyer theorem, applications and generalizations, moment maps in gauge theory, symplectic toric manifolds, Delzant's construction, and Duistermaat-Heckman theorems. The introduction provides an overview of the field, highlighting the historical development from classical mechanics to its current status as a rich and central branch of differential geometry and topology.This overview of symplectic geometry, written for the *Handbook of Differential Geometry*, covers the following topics: 1. **Symplectic Manifolds**: These are manifolds equipped with a symplectic form, a closed nondegenerate 2-form. Symplectic manifolds are necessarily even-dimensional and orientable. The chapter discusses basic properties, classical examples, equivalence notions, local normal forms, and symplectic submanifolds. 2. **Lagrangian Submanifolds**: These are submanifolds of symplectic manifolds of half dimension where the restriction of the symplectic form vanishes identically. The chapter describes normal neighborhoods of Lagrangian submanifolds and their applications. 3. **Complex Structures**: Any symplectic manifold admits almost complex structures, and these structures are compatible with the symplectic form. The chapter includes the local normal form for Kähler manifolds and a summary of Hodge theory. 4. **Symplectic Geography**: This topic concerns the existence and uniqueness of symplectic forms on a given manifold. It includes constructions of symplectic manifolds and invariants to distinguish them. 5. **Hamiltonian Geometry**: This geometry is concerned with symplectic manifolds equipped with a moment map, which is a collection of quantities conserved by symmetries. The chapter discusses the geometry of moment maps, including the classical Legendre transform, integrable systems, and convexity. 6. **Symplectic Reduction**: This is a fundamental tool in symplectic arguments, with infinite-dimensional analogues that have significant consequences for differential geometry. The chapter covers the Marsden-Weinstein-Meyer theorem, applications and generalizations, moment maps in gauge theory, symplectic toric manifolds, Delzant's construction, and Duistermaat-Heckman theorems. The introduction provides an overview of the field, highlighting the historical development from classical mechanics to its current status as a rich and central branch of differential geometry and topology.