A geometric approach to study quantum entanglement is advocated. We discuss first the geometry of the set of mixed quantum states acting on a finite dimensional Hilbert space. Next we consider bipartite quantum system and analyze the set containing separable mixed states. Studying geometric properties of this set contributes to our understanding of quantum entanglement and its time evolution. Vulnerability of entanglement due to quantum noise and destruction of quantum information due to interaction with an environment form key questions concerning feasibility of quantum computers.