The luminosity function of galaxies.

Galactic luminosity functions (LFs) and their applications in cosmological computations are discussed in an analytical review. The history and definitions of general and more specific LFs are recalled, and it is argued that the general LF is not universal and hence of only limited value. Particular attention is given to the relationship between LF and density function, the magnitudes employed, the selection of galaxies, and methods for determining the LF for field and cluster galaxies. Recent determinations of the galactic LF, for field and cluster galaxies, over all Hubble types and for different Hubble types, and for different environments are then surveyed, and a number of outstanding theoretical and observational problems are indicated.