These notes were prepared for a series of intensive lectures delivered at Hokkaido University, Nagoya University, Kyoto University, and Kyushu University. We begin with a brief review of higher-form symmetries, anomalies, and discrete gauge theories, before introducing non-invertible symmetries in (1+1)-dimensional systems. The basic structure of fusion categories is then discussed, including a discussion of categorical analogs of discrete gauging and representation theory. We subsequently turn to (3+1)-dimensional theories, where several physical applications of non-invertible symmetries are discussed. These notes are intended to be largely self-contained, and require no prior familiarity with subjects such as conformal field theory or lattice models.