Lecture 1: Preference and Graph Aggregation. This lecture will be an introduction to voting theory and preference aggregation using the axiomatic method. We will cover a number of basic aggregation rules, the Condorcet paradox, May's Theorem, and Arrow's Theorem. In the final part of the lecture we will discuss recent work on generalising the framework of preference aggregation to graph aggregation, which besides modelling elections also has applications in fields such a clustering and abstract argumentation.