Lie Theory is a branch of mathematics that studies Lie groups and Lie algebras, which are structures that describe continuous symmetries. These concepts are named after the mathematician Sophus Lie, who developed them in the 19th century. Lie groups are groups that are also smooth manifolds, allowing for the analysis of their properties using calculus. Lie algebras are associated with Lie groups and provide a way to study their infinitesimal transformations. They consist of elements that can be combined using a binary operation called the Lie bracket. Lie Theory has applications in various fields, including physics, particularly in the study of symmetry in quantum mechanics and general relativity.