A Lie Group is a mathematical structure that combines algebraic and geometric concepts. It consists of a set of continuous transformations that can be smoothly combined, allowing for the study of symmetry in various mathematical and physical systems. Lie groups are named after the mathematician Sophus Lie, who developed the theory in the 19th century. These groups are essential in many areas of mathematics and physics, particularly in understanding differential equations and quantum mechanics. They provide a framework for analyzing continuous symmetries, which can simplify complex problems and reveal underlying structures in various fields, including geometry and theoretical physics.