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 two key properties: bilinearity and the Jacobi identity. Lie algebras are essential in various areas of mathematics and physics, particularly in the study of group theory and quantum mechanics. Lie algebras can be classified into different types, such as semisimple and abelian algebras, based on their structure and properties. They play a crucial role in understanding continuous symmetries and are closely related to Lie groups, which represent symmetries in a geometric context.