A Lie Algebra is a mathematical structure that studies the properties of symmetry and transformations. It consists of a vector space equipped with a binary operation called the Lie bracket, which satisfies certain properties, such as bilinearity, antisymmetry, and the Jacobi identity. Lie algebras are essential in various fields, including physics and geometry, as they help describe the algebraic structures underlying continuous symmetries. Lie algebras are closely related to Lie Groups, which are groups that are also smooth manifolds. The study of Lie algebras allows mathematicians and physicists to analyze the infinitesimal transformations of these groups. Notable examples include the algebra of angular momentum in quantum mechanics and the algebra associated with the symmetry of geometric objects.