This repository contains a handout for a seminar talk about the quantum group $\mathrm{U}_q(\mathfrak{sl}_2)$. This talk was part of a Graduate Seminar on Representation Theory about Hopf algebras and tensor categories at the University of Bonn in the winter term of 2019/20. Since the talk some typos and minor mistakes have been fixed. In case of further typos or mistakes please contact me at stelzner@uni-bonn.de.

The document consists of two parts. The first part is the actual handout. The second part consists of two appendices. These appendices provide some of the proofs, remarks and additional content that had to be cut from the actual handout due to time constraints A table of contents can be found at the end of the document.

Click HERE for the PDF-version.