This textbook introduces geometric measure theory through the notion of
currents. Currents, continuous linear functionals on spaces of
differential forms, are a natural language in which to formulate types
of extremal problems arising in geometry, and can be used to study
generalized versions of the Plateau problem and related questions in
geometric analysis. Motivating key ideas with examples and figures, this
book is a comprehensive introduction ideal for both self-study and for
use in the classroom. The exposition demands minimal background, is
self-contained and accessible, and thus is ideal for both graduate
students and researchers.