  We have pioneered a new method for the measurement of extragalactic
distances. This method uses the time-lag between variations in the short
wavelength and long wavelength light from an active galactic nucleus (AGN),
based on a quantitative physical model of dust reverberation that relates the
time-lag to the absolute luminosity of the AGN. We use the large homogeneous
data set from intensive monitoring observations in optical and near-infrared
wavelength bands with the dedicated 2-m MAGNUM telescope to obtain the
distances to 17 AGNs in the redshift range z=0.0024 to z=0.0353. These distance
measurements are compared with distances measured using Cepheid variable stars,
and are used to infer that H_0= 73 +- 3 (random) km/s/Mpc. The systematic error
in H_0 is examined, and the uncertainty in the size distribution of dust grains
is the largest source of the systematic error, which is much reduced for a
sample of AGNs for which their parameter values in the model of dust
reverberation are individually measured. This AGN time-lag method can be used
beyond 30 Mpc, the farthest distance reached by extragalactic Cepheids, and can
be extended to high-redshift quasi-stellar objects.
