For some time it has been recognized that there is a marked similarity between superfluid helium and superconductors. The chief characteristic of both is their ability to sustain particle currents at a constant velocity for long periods of time without any driving force. To describe the condensed particles in either system, this book uses a macroscopic wave function and aims to show how the macroscopic theories of liquid 4He and metallic superconductors can be developed in parallel. Throughout the book those features of the two systems that can be described from a common viewpoint are emphasized. Also included in the book are a chapter covering both experimental and theoretical work on superfluid 3He and pointing out the analogies with other superfluid systems, and a new chapter on ceramic superconductors or "high-temperature superconductors". The aim of the book is to give an up-to-date summary at the time of writing of the work that seems likely to be of continuing importance. The text is intended for use by postgraduate students beginning research in either experimental or theoretical low-temperature physics and it is also intended to be accessible to undergraduates taking specialist courses in low-temperature physics.