This course-based primer provides newcomers to the field with a concise introduction
to some of the core topics in the emerging field of topological band insulators in
one and two dimensions. The aim is to provide a basic understanding of edge states,
bulk topological invariants, and of the bulk--boundary correspondence with as simple
mathematical tools as possible. We use noninteracting lattice models of topological
insulators, building gradually on these to arrive from the simplest one-dimensional
case (the Su-Schrieffer-Heeger model for polyacetylene) to two-dimensional time-reversal
invariant topological insulators (the Bernevig-Hughes-Zhang model for HgTe). In each
case the model is introduced first and then its properties are discussed and subsequently
generalized. The only prerequisite for the reader is a working knowledge in quantum
mechanics, the relevant solid state physics background is provided as part of this
self-contained text, which is complemented by end-of-chapter problems.
