On the dunford and pettis integrals.- Real semigroups in commutative banach algebras.- Brownian motion and UMD-spaces.- Lectures on the central limit theorem for empirical processes.- Some applications of vector-valued analytic and harmonic functions.- Differentiability properties of vector valued functions.- Malliavin calculus and stochastic integrals.- Martingale and integral transforms of banach space valued functions.