In this mini course, I shall introduce the basic concepts in 2D topological orders by studying simple models of topological orders and then introduce topological quantum computing based on Fibonacci anyons. Here is the (not perfectly ordered) syllabus.
Overview of topological phases of matter
Z2 toric code model: the simplest model of 2D topological orders
Quick generalization to the quantum double model
Anyons, topological entanglement entropy, S and T matrices
Fusion and braiding of anyons: quantum dimensions, pentagon and hexagon identities