The book covers three main strands, Bose-Einstein condensates (BEC), superfluids and superconductivity. The subjects are developed in a way which gradually builds up the key concepts and the necessary mathematical machinery. The book begins with the simplest of the three topics, BEC, and first thoroughly reviews the basics of the Bose-Einstein ideal gas before going into the techniques of magnetic trapping and cooling of atoms and the discovery of BEC in dilute atomic gases. Superfluidity in helium-4 is more difficult to understand, because it is a strongly interacting quantum liquid. The book introduces the main physical phenomena of superfluidity, and how it follows from the key concept of macroscopic quantum coherence and off-diagonal long ranged order. The theory of superconductivity is developed in stages, starting with the simpler London and Ginzburg Landau theories and their main applications, before developing the mathematical concepts of a quantum coherent state and the Bardeen Cooper Schrieffer (BCS) theory. The final chapter deals with the more advanced topics, including superfluid helium-3 and evidence for unconventional Cooper pairing in exotic superconductors. No prior knowledge of quantum many-body theory is assumed, and the necessary mathematical concepts are introduced in a self-contained manner where needed.
