Abstract This introductory chapter begins with a discussion of quantum solids and liquids. It then discusses Fermi gas and liquid, superfluid, and magnetic solid.
Abstract Four different systems, mostly of recent vintage, which are known or conjectured to manifest BEC/Cooper pairing are discussed. First, various non-cuprate “exotic” superconductors (alkali fullerides, organics, heavy fermions, ruthenates) are reviewed. Next, an account is given of the superfluid phases of liquid 3He in the pores of aerogel. A third section introduces the topic of the “supersolid” behavior recently reported in solid 4He, and comments on some theoretical issues raised by the experiments. The last section of the chapter considers the newly realized system of ultracold Fermi alkali gases, where one can study experimentally the apparently smooth crossover between the BEC of diatomic molecules and BCS superfluidity in a degenerate Fermi gas, thus unifying the concepts of BEC and Cooper pairing.