This course will cover the basics of algebraic number theory from a concrete point of view, with an eye to applications (e.g., to Diophantine equations and cryptography). The first few weeks of the course will survey aspects of field theory, mostly as dictated by what will be needed for algebraic number theory. The rest of the course will cover algebraic number fields; although the ideas will be developed for general number fields, there will be substantial focus on fields of small degree, and on explicit computations.