We present maps of a 14 pc * 20 pc region covering the Sgr B2 molecular cloud complex in the 13CO (1 - 0) and CS (1 - 0) lines with high angular resolution. A more restricted central area was also mapped in the C18O (1 - 0) line. The 13CO cloud consists of two components: a compact core of 3 pc in diameter roughly centered on Sgr B2 (M) and an extended plateau of 17 pc * 7.5 pc area containing the maser sources and most of the HII regions. Compact, massive ( 3 * 105 M_o) C18O cores are associated with Sgr B2(M) and Sgr B2(N). The obtained intensity distributions are compared with those of molecular masers and compact HII regions reported in the literature. Low-velocity (40 - 65 km s-1) masers, with positions roughly aligned in the north-south line connecting the three major compact HII region complexes, are located near the eastern margin of a large hole in the low-velocity molecular cloud. In contrast, most of the high-velocity (65 - 80 km s-1) masers are distributed near the center of a compact molecular cloud at higher velocity, where a shock seems to have occurred. These results provide further evidence supporting the cloud-cloud collision hypothesis based on limited 13CO (1 - 0) data (Hasegawa et al. 1994). In addition, this hypothesis appears to be consistent with a wide range of new observations that have appeared in the literature.