  The local (v<1200kms) and the cosmic expansion field out to 30000kms-1 are
characterized by Ho=58. While the random error is small (+-2), it may still be
affected by systematic errors as large as 10%. The local expansion is outlined
by Cepheids and by Cepheid-calibrated TF distances of a complete sample of
field galaxies and by nearby groups and clusters; the cosmic expansion is
defined by Cepheid-calibrated SNeIa. The main source of systematic errors are
therefore the shape and the zero point of the P-L relation of Cepheids and its
possible dependence on metallicity. GAIA will essentially eliminate these error
sources. Another source of systematic error is due to the homogenization of
SNeIa as to decline rate Delta m_15 and color (B-V). GAIA will discover about
half of the 2200 SNeIa which will occur during a four-year lifetime within
10000kms. For many of them ground-based follow-up will provide useful
photometric parameters (and spectra), which will allow to fix the dependence of
the SNeIa luminosity on Delta m_15 and (B-V) with high accuracy. At the same
time they will yield exquisite distances to an corresponding number of field
galaxies. - GAIA will also revolutionize the very local distance scale by
determining fundamental distances of the companion galaxies of the Milky Way
and even of some spirals in- and possibly outside the Local Group from their
rotation curves seen in radial velocities and proper motions. Moreover, GAIA
will obtain trigonometric parallaxes of RR Lyrae stars, of red giants defining
the TRGB, of stars on the ZAMS, of White Dwarf defining their cooling sequence,
and of globular clusters, and determine the metallicity dependence of these
distance indicators. It will thus establish a self-controlling network of
distance indicators within the Local Group and beyond.
