Lie groups and their corresponding algebras are ubiquitous in theoretical physics and the mathematical formulation of nature. These lectures will provide an overview of the theory of lie groups and lie algebras, motivated by their role in the physical context. We begin by developing the formalism of basic group theory, followed by an introduction into representation theory. This is followed by an in-depth discussion of algebras, along with their properties and representations. Numerous examples, including from (but not limited to) particle physics, quantum mechanics, computational chemistry, and structural biology, will be considered. We will conclude with an exposition into differential geometry, highlighting group manifold structures. If time allows, we will explore symplectic geometry and the connection between classical/quantum mechanics via lie groups.
