The lectures this volume collects were designed for an audience having basic knowledge of Functional Analysis and Measure Theory, but not familiar with Probability. The main aim is to give an introduction to Analysis in separable infinite-dimensional Hilbert spaces. The arguments the book deals with are: Gaussian measures, reproducing kernels, Cameron-Martin formula, Brownian motion, Wiener integral, invariant measures, ergodicity, mixing, Ito-Wiener decomposition.