I will first give an introduction to Computational Social Choice and Voting Theory to set the context for discussing Liquid Democracy. Liquid Democracy is a voting framework in which voters can decide to either vote on an issue directly or to delegate their vote to other voters. As such it can be seen as a hybrid between Direct Democracy and Representative Democracy. While Liquid Democracy aims at overcoming certain problems of these two more traditional types of democracy, it brings it's own types of problems with it. As theoretical computer scientists we are interested in formalising desiderata (e.g., that voters cannot manipulate the system) and design mechanisms that enforce these. An analysis of these algorithms for Liquid Democracy typically comes with a graph theoretical flavour. I will present work in progress on the specific case, where voters are allowed to specify several delegation possibilities in form of a ranking.