The connected closed Subgroups (up to an Isomorphism) of Complex Matrices that are closed under conjugate transpose and have a discrete finite center. Examples include Special Linear Groups, Symplectic Groups, and certain isometry groups of Quadratic Forms.
See also Lie Group
Knapp, A. W. ``Group Representations and Harmonic Analysis, Part II.'' Not. Amer. Math. Soc. 43,