This textbook deals with the central areas of a measure-theoretic approach to probability theory, covering the scope of a two-semester lecture. After the fundamentals, limit theorems and weak convergence are discussed. This is followed by the presentation and examination of stochastic dependence through conditional expectation, which is realized with the Radon-Nikodym derivative. It is applied to the theory of stochastic processes, which consists of the general construction from the study of martingales and Markov processes. New in a textbook on general probability theory is an introduction to stochastic analysis of semimartingales based on a suitable continuity condition, with applications to the theory of financial markets. The book contains numerous exercises, some with solutions. In addition to the theory, it deepens understanding through applications.