  The first results of the construction of a 3D reddening map for stars within
1600 pc of the Sun are presented. Analysis of the distribution of 70 million
stars from the 2MASS catalog with the most accurate photometry on the (J-Ks) -
Ks diagram supplemented with Monte Carlo simulations has shown that one of the
maxima of this distribution corresponds to F-type dwarfs and subgiants with a
mean absolute magnitude MKs=2.5m. The shift of this maximum toward large (J-Ks)
with increasing $Ks$ reflects the reddening of these stars with increasing
heliocentric distance. The distribution of the sample of stars over Ks, l, and
b cells with corresponds to their distribution over 3D spatial cells. As a
result, the reddening E(J-Ks) has been determined with an accuracy of 0.03m for
spatial cells with a side of 100 pc. All of the known large absorbing clouds
within 1600 pc of the Sun have manifested themselves in the results obtained.
The distances to the near and far edges of the clouds have been determined with
a relative accuracy of 15\%. The cases where unknown clouds are hidden behind
known ones on the same line of sight have been found. The distance dependence
of reddening is considered for various Galactic latitudes and longitudes. The
absorbing matter of the Gould Belt is shown to manifest itself at latitudes up
to 40 deg and within 600 pc of the Sun. The size and influence of the Gould
Belt may have been underestimated thus far. The absorbing matter at latitudes
up to 60 deg and within 1600 pc of the Sun has been found to be distributed
predominantly in the first and second quadrants in S hemisphere and in the
third and fourth quadrants in N hemisphere. A nonrandom orientation of the
clouds relative to the Sun is possible. The mass of the baryonic dark matter in
solar neighborhoods can then be considerably larger than is generally believed.
