  An introductory survey of the theoretical ideas and calculations and the
experimental results which depart from Landau Fermi-liquids is presented.
Common themes and possible routes to the singularities leading to the breakdown
of Landau Fermi liquids are categorized following an elementary discussion of
the theory. Soluble examples of Singular Fermi liquids (often called Non-Fermi
liquids) include models of impurities in metals with special symmetries and
one-dimensional interacting fermions. A review of these is followed by a
discussion of Singular Fermi liquids in a wide variety of experimental
situations and theoretical models. These include the effects of low-energy
collective fluctuations, gauge fields due either to symmetries in the
hamiltonian or possible dynamically generated symmetries, fluctuations around
quantum critical points, the normal state of high temperature superconductors
and the two-dimensional metallic state. For the last three systems, the
principal experimental results are summarized and the outstanding theoretical
issues highlighted.
