  These are lecture notes written at the University of Zurich during spring
2014 and spring 2015. The first part of the notes gives an introduction to
probability theory. It explains the notion of random events and random
variables, probability measures, expectation, distributions, characteristic
function, independence of random variables, types of convergence and limit
theorems. The first part is separated into two different chapters. The first
chapter is about combinatorial aspects of probability theory and the second
chapter is the actual introduction to probability theory, which contains the
modern probability language. The second part covers conditional expectations,
martingales and Markov chains, which are easily accessible after reading the
first part. The chapters are exactly covered in this order and go into some
more details of the respective topic.
