Dedekind sums

Dedekind sums arose out of the study of elliptic functions and modular forms. They were iniially discovered by Dedekind but have since been studied for their many arithmetic properties. Much work has been done on Dedekind sums and in 1972 Rademacher and Grosswald released a book that summarised much of what was known, as well as providing a history of Dedekind sums. This encouraged greater interest in this topic and provided groundwork for further research. In our essay we seek to update Rademacher and Grosswald's book by providing an overview of some of the research that has been done since its publication. We will also extend some results of Myerson and Phillips, regarding fixed points of Dedekind sums. It is our intention that our findings will provide a foundation for future research in the study of Dedekind sums.