As teaching material for this course we will primarily use the book "Functional Analysis" by Gerald Teschl. This book is available online. You can dowload a pdf-version of it here. We will go through the chapters 1-5 in Teschl's book.
In addition, we will cover some Fourier analysis. I plan to write a short set of lecture notes for this part of the course.
Further, the exercises in Teschl's book will be supplemented by additional exercises. These will be announced on the course homepage, under the detailed teaching plan.