We have reached the point where we are ready to introduce the main object of our investigation: sub-Riemannian manifolds and, more generally, sub-Finsler manifolds, also known as Carnot-Carathéodory spaces. These spaces will be equipped with Carnot-Carathéodory distances. Our first significant result is the Chow-Rashevsky Theorem, which states that on every sub-Finsler manifold, the Carnot-Carathéodory distance induces the same topology as the manifold structure itself. It is important to emphasize that this result relies on the crucial assumption that the horizontal vector fields and their brackets generate all possible directions.