In these notes we provide a straightforward introduction to the topic of harmonic measure.
This is an area where many advances have been obtained in the last years and we think
that this book can be useful for people interested in this topic.

In the first Chapters 2-6 we have followed classical references such as [Fol95], [Car98],
[GM05], [Lan72], [AG01], and [Ran95], as well as some private notes of Jonas Azzam. A
large part of the content of Chapter 7 is based on Kenig’s book [Ken94], and on papers by
Aikawa, Hofmann, Martell, and many others. Chapter 8 is based on a paper by Jerison
and Kenig [JK82]. In Chapter 9, the proof of Jones-Wolff theorem about the dimension
of harmonic measure in the plane follows the presentation of [CTV18]. In some parts of
Chapter 10 we follow the book of Caffarelli and Salsa [CS05] and some work by Mourgoglou
and the second named author of these notes. A large part of Chapter 11 follows [AHM’16].

We apologize in advance for possible inaccuracies or lack of citation. Anyway, we remark
that this work is still under construction and we plan to add more content as well as more
accurate citations in future versions of these notes.