I will introduce the notion of volume entropy of a Riemannian manifold and establish a relationship with the topological entropy of the manifold. I plan to sketch Manning's proof of the equality of these two entropies under the assumption of non-positive sectional curvature. To illustrate the importance of this concept of volume entropy, I will try to discuss a theorem due to Besson, Courtois and Gallot. Among other things, it will show that on a manifold, the locally symmetric metric of negative curvature is uniquely determined by two numbers - its volume entropy and volume. Speaker(s): Mitul Islam (UM)