  Poincar\'e's Polyhedron Theorem is a widely known valuable tool in
constructing manifolds endowed with a prescribed geometric structure. It is one
of the few criteria providing discreteness of groups of isometries. This work
contains a version of Poincar\'e's Polyhedron Theorem that is applicable to
constructing fibre bundles over surfaces and also suits geometries of
nonconstant curvature. Most conditions of the theorem, being as local as
possible, are easy to verify in practice.
