So far almost sure convergence, convergence in probability, and convergence in Lp of random variables were considered. All these types of convergence require that the convergent sequence of random variables is defined on the same probability space. This is relaxed by the weak convergence, where one only considers the convergence of the laws of the random variables. Main results about weak convergence, like the so-called Portmanteau theorem, Levy’s continuity theorem, Prokhorov’s theorem, and the continuous mapping theorem are proven. Finally it is shown that the theorem of Dudley and Skorohod provides a way back to the notion of almost sure convergence.