The space of probability measures with finite second moment, once endowed with the \(W_2\) distance, has the structure of a metric space. It has in fact a much richer geometric structure, as it resembles a Riemannian manifold. Consequently, we can bring to bear the calculation rules of Riemannian geometry, known in this context as Otto calculus, on the design and interpretation of algorithms over the space of probability measures. Our main goal in constructing this formalism is to define interesting dynamics on the Wasserstein space, given by gradient flows.