  We apply the GBDT version of the B\"acklund-Darboux transformation to the
nonlocal NLS (focusing and defocusing cases). The matrix case is included and
solutions in the form of rectangular $m_1 \times m_2$ matrix functions are
dealt with. The wave function is also constructed explicitly. Families of
explicit examples are considered in detail. Some initial results and
representations for the more complicated algebro-geometric solutions are
obtained as well.
