  This in an introduction to free probability theory, covering the basic
combinatorial and analytic theory, as well as the relations to random matrices
and operator algebras. The material is mainly based on the two books of the
lecturer, one joint with Nica and one joint with Mingo. Free probability is
here restricted to the scalar-valued setting, the operator-valued version is
treated in the subsequent lecture series on "Non-Commutative Distributions".
The material here was presented in the winter term 2018/19 at Saarland
University in 26 lectures of 90 minutes each. The lectures were recorded and
can be found online at
https://www.math.uni-sb.de/ag/speicher/web_video/index.html
