  The AMIGA project (Analysis of the Interstellar Medium of Isolated Galaxies)
is compiling a multiwavelength database of isolated galaxies that includes
optical (B and Halpha), infrared (FIR and NIR) and radio (continuum plus HI and
CO lines) properties. It involves a refinement of the pioneering Catalog of
Isolated Galaxies. This paper is the first in a series and begins with analysis
of the global properties of the nearly redshift-complete CIG with emphasis on
the Optical Luminosity Function (OLF) which we compare with other recent
estimates of the OLF for a variety of environments. The CIG redshift
distribution for n= 956 galaxies re-enforces the evidence for a bimodal
structure seen earlier in smaller samples. The peaks at redshift near 1500 and
6000km/s correspond respectively to galaxies in the local supercluster and
those in more distant large-scale components (particularly Perseus-Pisces). The
two peaks in the redshift distribution are superimposed on 50% or more of the
sample that is distributed in a much more homogeneous way. The CIG probably
represents the most homogeneous local field example that has ever been
compiled. Our derivation of the CIG OLF is consistent with other studies of the
OLF for lower density environments. This comparison via the Schechter parameter
formalization shows that: 1) M* increases with galaxy surface density on the
sky and 2) alpha shows a weaker tendency to do the same. The CIG represents the
largest and most complete foundation for studies of isolated galaxies and is
likely as close as we can come to a field sample. (Tables 1, 2 and 3 are
available in electronic form at http://www.iaa.es/AMIGA.html).
