This book is a short but complete introduction to the Loewner equation and the SLEs which
are a family of random fractal curves as well as the relevant background in probability and
complex analysis. The connection to statistical physics is also developed in the text in an
example case. The book is based on a course (with the same title) lectured by the author. First
three chapters are devoted to the background material but at the same time give the reader a
good understanding on the overview on the subject and on some aspects of conformal invariance.
The chapter on the Loewner equation develops in detail the connection of growing hulls and the
differential equation satisfied by families of conformal maps. The Schramm-Loewner evolutions
are defined and their basic properties are studied in the following chapter and the regularity
properties of random curves as well as scaling limits of discrete random curves are
investigated in the final chapter. The book is aimed at graduate students or researchers who
want to learn the subject fairly quickly.
