  Given an arbitrary hypergraph $\mathcal{H}$, we may glue to $\mathcal{H}$ a
family of hypergraphs to get a new hypergraph $\mathcal{H}'$ having
$\mathcal{H}$ as an induced subhypergraph. In this paper, we introduce three
gluing techniques for which the topological and combinatorial properties (such
as Cohen-Macaulayness, shellability, vertex-decomposability etc.) of the
resulting hypergraph $\mathcal{H}'$ is under control in terms of the glued
components. This enables us to construct broad classes of simplicial complexes
containing a given simplicial complex as induced subcomplex satisfying nice
topological and combinatorial properties. Our results will be accompanied with
some interesting open problems.
