In these notes we provide a straightforward introduction to the topic harmonic measure. This is an area were 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 2-7 we have followed classical references such as [Fol95], [Car98], [GM05], [Lan72], and [Ran95], as well as some private notes of Jonas Azzam. The content of Chapter 8 is based on Kenig’s book [Ken94], and on papers by Aikawa, Hofmann, Martell, and many others. Chapter 9 is based on a paper by Jerison and Kenig [JK82], while 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. Most of the last chapter 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.