  We report a three year, 18 epoch, VLBI monitoring study of H2O masers in the
sub-parsec, warped, accretion disk within the NGC4258 AGN. Our immediate goals
are to trace the geometry of the underlying disk, track rotation via
measurement of proper motion, and ascertain the radii of masers for which
centripetal acceleration may be measured separately. The monitoring includes ~
4 times as many epochs, ~ 3 times denser sampling, and tighter control over
sources of systematic error than earlier VLBI investigations. Coverage of a ~
2400 km/s bandwidth has also enabled mapping of molecular material ~ 30% closer
to the black hole than accomplished previously, which will strengthen geometric
and dynamical disk models. Through repeated observation we have also measured
for the first time a 5 microarsecond (1 sigma) thickness of the maser medium.
Assuming this corresponds to the thickness of the accretion disk, hydrostatic
equilibrium requires a disk plane temperature of ~ 600 K. Our long-term goal is
a geometric distance to NGC4258 that is accurate to ~ 3%, a ~ 2 times
improvement over the current best estimate. A geometric estimate of distance
can be compared to distances obtained from analysis of Cepheid light curves,
with the intent to recalibrate the extragalactic distance scale with reduced
systematic uncertainties. This is the first paper in a series. We present here
VLBI observations, data reduction, and temporal and spatial characteristics of
the maser emission. Later papers will report estimation of orbital acceleration
and proper motion, modeling of disk 3-D geometry and dynamics, and estimation
of a "maser distance." Estimation of a "Cepheid distance" is presented in a
parallel paper series.
