Semi-algebras and sigma-algebras of events, Kolmogorov?s axioms of probability, consequences thereof, probability spaces, measurability, random variables as measurable mappings, random vectors, probability measures induced on Borel sigma-algebras by random vectors, distributions and distribution functions, extension of probability measure starting by semi-algebras, mathematical expectation, expected values of non-negative simple, non-negative and general random variables, properties, conditional distributions and independence, Borel-Cantelli lemma, conditional expectation given a sub sigma-algebra, Radon-Nikodym theorem, different modes of convergence, almost sure convergence, convergence in probability, convergence in L^p, convergence in distribution, different implications between them, characteristic functions, inversion formulas, relation to convergence concepts, the weak and the strong law of large numbers, central limit theorem.