  Effective theories of quantum liquids (superconductors and superfluids of
various types) are derived starting from microscopic models at the absolute
zero of temperature. Special care is taken to assure Galilei invariance. The
effective theories are employed to investigate the quantum numbers carried by
the topological defects present in the phases with spontaneously broken
symmetries. Due to topological terms induced by quantum fluctuations, these
numbers are sometimes found to be fractional. The zero-temperature effective
theories are further used to study the quantum critical behavior of the
liquid-to-insulator transition which these systems undergo as the applied
magnetic field, the amount of impurities, or the charge carrier density varies.
The classical, finite-temperature phase transitions to the normal state are
discussed from the point of view of dual theories, where the defects of the
original formulation become the elementary excitations. A connection with
bosonization is pointed out.
