Symmetry is a fundamental concept in physics, often described by continuous groups called Lie groups. These groups are smooth manifolds with a group structure, and their tangent spaces form Lie algebras, which encode important properties of the group. In quantum mechanics, symmetries are represented by unitary or projective representations of Lie groups on Hilbert spaces. The Lie algebra of a group gives rise to a corresponding Lie algebra representation, which is easier to work with. The commutativity of the Hamiltonian with the rotation group's representation implies that energy eigenspaces are rotationally invariant, a concept used in determining the hydrogen atom's energy eigenvectors. This chapter provides an overview of Lie groups, Lie algebras, and their representations, focusing on matrix Lie groups as closed subgroups of GL(n;C). The Lie algebra of a group is a real vector space with a bracket operation, defined by [X, Y] = XY - YX. This algebraic structure captures much of the group's information and simplifies computations. Unitary representations of Lie groups are continuous homomorphisms into the unitary operator group on a Hilbert space. For finite-dimensional Hilbert spaces, each group representation gives rise to a Lie algebra representation. However, not all Lie algebra representations come from group representations, except when the group is simply connected. This chapter lays the groundwork for later studies on angular momentum and the hydrogen atom.Symmetry is a fundamental concept in physics, often described by continuous groups called Lie groups. These groups are smooth manifolds with a group structure, and their tangent spaces form Lie algebras, which encode important properties of the group. In quantum mechanics, symmetries are represented by unitary or projective representations of Lie groups on Hilbert spaces. The Lie algebra of a group gives rise to a corresponding Lie algebra representation, which is easier to work with. The commutativity of the Hamiltonian with the rotation group's representation implies that energy eigenspaces are rotationally invariant, a concept used in determining the hydrogen atom's energy eigenvectors. This chapter provides an overview of Lie groups, Lie algebras, and their representations, focusing on matrix Lie groups as closed subgroups of GL(n;C). The Lie algebra of a group is a real vector space with a bracket operation, defined by [X, Y] = XY - YX. This algebraic structure captures much of the group's information and simplifies computations. Unitary representations of Lie groups are continuous homomorphisms into the unitary operator group on a Hilbert space. For finite-dimensional Hilbert spaces, each group representation gives rise to a Lie algebra representation. However, not all Lie algebra representations come from group representations, except when the group is simply connected. This chapter lays the groundwork for later studies on angular momentum and the hydrogen atom.