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