Superfluidity - and closely related to it, superconductivity - are very general phenomena that can occur on vastly different energy scales. Their underlying theoretical mechanism of spontaneous symmetry breaking is even more general and applies to a multitude of physical systems.

In these lecture notes, a pedagogical introduction to the field-theory approach to superfluidity is presented. The connection to more traditional approaches, often formulated in a different language, is carefully explained in order to provide a consistent picture that is useful for students and researchers in all fields of physics.

After introducing the basic concepts, such as the two-fluid model and the Goldstone mode, selected topics of current research are addressed, such as the BCS-BEC crossover and Cooper pairing with mismatched Fermi momenta.

Introduction.- Superfluid Helium.- Superfluidity in Quantum Field Theory.- Relativistic Two-Fluid Formalism.- Fermionic Superfluidity: Cooper Pairing.- Meissner Effect in a Superconductor.- BCS-BEC Crossover.- Low-Energy Exitations in a Fermionic Superfluid.- Cooper-Pairing with Mismatched Fermi Momenta.- References.