These are my notes on the lecture Probability Theory, taught by Prof.~\textsc{Chiranjib Mukherjee} in the summer term 2023 at the University Münster. \begin{warning} This is not an official script. The official lecture notes can be found on \href{https://sso.uni-muenster.de/LearnWeb/learnweb2/course/view.php?id=67595#coursecontentcollapse1}{Learnweb}. \end{warning} These notes contain errors almost surely. If you find some of them or want to improve something, please send me a message:\\ \texttt{notes\_probability\_theory@jrpie.de}. \paragraph{Topics of this lecture} \begin{enumerate}[(1)] \item Limit theorems: Laws of large numbers and the central limit theorem for i.i.d.~sequences, \item Conditional expectation and conditional probabilities, \item Martingales, \item Markov chains. \end{enumerate} This notes follow the way the material was presented in the lecture rather closely. Additions (e.g.~from exercise sheets) and slight modifications have been marked with $\dagger$.