Lecture Notes Spectral Theory

These lecture notes are based on my course from the summer semester 2015. I kept the numbering and the contents of the results presented in the lectures (except for minor corrections and improvements). Typically, the proofs and calculations in the notes are a bit shorter than those given in the lecture. Moreover, the drawings and many additional, mostly oral remarks from the lectures are omitted here. On the other hand, I have added several lengthy proofs not shown in the lectures (mainly about Sobolev spaces). These are indicated in the text. I like to thank Bernhard Konrad for his support in preparing the version of these lecture notes from 2010 and Heiko Hoffmann and Martin Meyries for several corrections and comments.