# Introduction to compact and discrete quantum groups

## TL;DR

This paper provides an introductory overview of compact and discrete quantum groups, explaining their mathematical foundations and duality relationships, based on graduate lectures.

## Contribution

It offers a clear, accessible introduction to the theory of compact and discrete quantum groups, bridging Hopf algebras and topological quantum groups.

## Key findings

- Explains the transition from Hopf algebras to compact quantum groups
- Sketches the duality between compact and discrete quantum groups
- Provides foundational knowledge for further study in quantum group theory

## Abstract

These are notes from introductory lectures at the graduate school "Topological Quantum Groups" in B\k{e}dlewo (June 28--July 11, 2015). The notes present the passage from Hopf algebras to compact quantum groups and sketch the notion of discrete quantum groups viewed as duals of compact quantum groups.