The product of the previously constructed 3D maps of stellar reddening (Gontcharov, 2010AstL...36..584G, Cat. J/PAZh/36/615) and Rv variations (Gontcharov, 2012AstL...38...12G, J/PAZh/38/15) has allowed us to produce a 3D interstellar extinction map within the nearest kiloparsec from the Sun with a spatial resolution of 100pc and an accuracy of 0.2m. This map is compared with the 2D reddening map by Schlegel et al. (1998ApJ...500..525S), the 3D extinction map at high latitudes by Jones et al. (2011AJ....142...44J), and the analytical 3D extinction models by Arenou et al. (1992A&A...258..104A) and Gontcharov (2009AstL...35..780G). In all cases, we have found good agreement and show that there are no systematic errors in the new map everywhere except the direction toward the Galactic center. We have found that the map by Schlegel et al. (1998ApJ...500..525S) reaches saturation near the Galactic equator at E(B-V)>0.8m, has a zero-point error and systematic errors gradually increasing with reddening, and among the analytical models those that take into account the extinction in the Gould Belt are more accurate. Our extinction map shows that it is determined by reddening variations at low latitudes and Rv variations at high ones. This naturally explains the contradictory data on the correlation or anticorrelation between reddening and Rv available in the literature. There is a correlation in a thin layer near the Galactic equator, because both reddening and Rv here increase toward the Galactic center. There is an anticorrelation outside this layer, because higher values of Rv correspond to lower reddening at high and middle latitudes. Systematic differences in sizes and other properties of the dust grains in different parts of the Galaxy manifest themselves in this way. The largest structures within the nearest kiloparsec, including the Local Bubble, the Gould Belt, the Great Tunnel, the Scorpius, Perseus, Orion, and other complexes, have manifested themselves in the constructed map. Also the data of the Rv from Gontcharov (2012AstL...38...12G, Cat. J/PAZh/38/15) and E(B-V) from Gontcharov (2010AstL...36..584G, Cat. J/PAZh/36/615) 3D maps are added. The error of the E(B-V) is 0.04mag. The error of the Rv is about 0.2.