A presymplectic structure on odd dimensional manifold is given by a closed
2-form which is nondegenerate, i.e., of maximal rank. We investigate geometry
of presymplectic manifolds. Some basic theorems analogous to those in
symplectic and contact topology are given and applied to study constructions of
presymplectic manifolds. In particular, we describe how to glue presymplectic
manifolds along a presymplectic submanifold, including surgery along a
presymplectic circles.