I will give an introduction to the theory of topological matter and anyons, and to the theory of topological quantum information and computation. I will discuss the following subjects: quantum braiding statistics and anyons, topological order, topological quantum codes, fractional quantum Hall systems, topological qubits and topological protection, topological quantum computation. I will introduce these concepts both at a mathematical level and at a physical level, discussing physical systems in which topological order and anyons can arise.