This mini-course will cover a range of topics related to random minimum spanning trees and, to a lesser extent, uniform spanning trees. It is possible the below lecture plan will be adjusted, either to cover necessary background material, or as a function of the interests of the audience.

- Day 1. Minimum spanning trees: Kruskal's algorithm (for matroids), Prim's algorithm, Cycle breaking. How things go wrong on infinite graphs. Uniform spanning trees: Matrix-based generation, Wilson's algorithm, Finite-dimensional distributions.