Symplectic geometry is a branch of mathematics that is concerned with the study of symplectic manifolds. It is a fundamental field in modern mathematics that deals with the geometry of classical mechanics. Synonyms for the term "symplectic geometry" include Hamiltonian geometry, canonical geometry or the geometry of phase space. These descriptions all refer to the same field that aims to study the mathematics behind conserving mechanical systems, such as the motion of planets. Despite the various terms used, symplectic geometry remains an essential area of study in the mathematical community, with its applications in physics, engineering, and computer science.