After a brief review of Hausdorff measures and rectifiable sets, I introduce two basic objects used in geometric measure theory to study minimal surfaces, namely varifolds and currents. We then cover some of the basic structure, compactness and approximation theorems and explore the classical regularity results for stationary varifolds (Allard's theorem) and area minimizing currents in codimension 1. The syllabus of the course is essentially the content of Leon Simon's Lectures in geometric measure theory, but for many parts we follow more recent alternative approaches to the material therein.