The measurement of galaxy distances is one of the most fundamental
problems in astronomy. To begin with, we would simply
like to know the scale of the cosmos; we do so by determining
the distances to galaxies. Beyond this, galaxy distances are the key
to measuring the Hubble constant H0, perhaps the
most important piece of information for testing the validity of the Big Bang
model. Finally, galaxy distances are necessary if we are to study
the large-scale peculiar velocity field. Peculiar velocity analysis is
among the most promising techniques for confirming
the gravitational instability paradigm for the origin of large-scale
structure, deducing the relative distributions of luminous and dark
matter, and constraining the value of the cosmological
density parameter 
0. In this Chapter, I will describe
a number of the methods used for measuring
galaxy distances, and discuss their application to
the H0 and peculiar velocity problems.
When appropriate, I will comment on their
relevance to determination of other cosmological parameters
as well. The goal of this Chapter is not to present
an exhaustive review of galaxy distance measurements,
but rather to provide a summary of where matters
stand, and an indication of what the
next few years may bring.