Construction of gravitational instantons with non-maximal volume growth

In this thesis, we construct families of gravitational instantons of type ALG, ALG*, ALH and ALH*. Away from a finite set of exceptional points, the metric collapses with bounded curvature to a quotient of R^3 by a lattice of rank one or two and Z_2. Depending on whether the gravitational instantons are of type ALG/ALG* or ALH/ALH*, there are two or four exceptional points respectively that are modelled on the Atiyah-Hitchin manifold. The other exceptional points are modelled on the Taub-NUT metric. There are at most four, respectively eight, of these points in each case. These gravitational instantons are constructed using a gluing construction, where we combine these ALF gravitational instantons to a bulk space that is constructed using the Gibbons-Hawking ansatz. We then set up a deformation argument, where we perturb these approximate solutions into genuine gravitational instantons