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 insulators. The aim is to provide a basic understanding of edge states, bulk topological invariants, and the bulk-boundary correspondence using simple mathematical tools. The approach utilizes noninteracting lattice models of topological insulators, gradually building from the simplest one-dimensional case (the Su-Schrieffer-Heeger model for polyacetylenes) to two-dimensional time-reversal invariant topological insulators (the Bernevig-Hughes-Zhang model for HgTe). In each case, the discussion of simple toy models is followed by the formulation of general arguments regarding topological insulators. The only prerequisite for the reader is a working knowledge of quantum mechanics and the relevant solid state physics.