This book is devoted to a theory of gradient flows in spaces which are not necessarily endowed with a natural linear or differentiable structure. It is made of two
parts, the first one concerning gradient flows in metric spaces and the second one
devoted to gradient flows in the L2-Wasserstein space of probability measures1 on
a separable Hilbert space X (we consider the Lp-Wasserstein distance, p ∈ (1,∞),
as well).