The purpose of this series of lectures is to describe joint work with Robert Berman where we investigate the relationship between tranfinite diameters and Monge-Ampere operators in the geometric context of compact complex manifolds endowed with a Hermitian holomorphic line bundle. The tranfinite diameter describes the growth of the sup-norm on the space of sections of large powers of the line bundle, and the goal is to express this quantity in terms of a natural energy functional which is well-known in Kahler geometry and is basically the primitive of the Monge-Ampere operator. Among other things, this point of view enables to extend the classical notion of logarithmic energy of a measure to the higher-dimensional setting and to get a variational characterization of equilibrium measures.