In the following chapter, we will review the theory of Lie groups. This revision serves two purposes: First, Lie groups equipped with special sub-Finsler structures appear as tangent spaces of Carnot-Carathéodory spaces. Such Lie groups serve as infinitesimal models for sub-Riemannian manifolds, playing the same role as Euclidean vector spaces in Riemannian geometry. Second, sub-Finsler structures on Lie groups are highly interesting and arise in various contexts, including geometric group theory, harmonic analysis, hyperbolic geometry, and furthermore in stochastic processes and mechanics. They are, in a sense, easier to study than general Carnot-Carathéodory spaces.