  In the first part of this thesis, Kerr-Schild metrics and extended
Kerr-Schild metrics are analyzed in the context of higher dimensional general
relativity. Employing the higher dimensional generalizations of the
Newman-Penrose formalism and the algebraic classification of spacetimes based
on the existence and multiplicity of Weyl aligned null directions, we establish
various geometrical properties of the Kerr-Schild congruences, determine
compatible Weyl types and in the expanding case discuss the presence of
curvature singularities. We also present known exact solutions admitting these
Kerr-Schild forms and construct some new ones using the Brinkmann warp product.
In the second part, the influence of quantum corrections consisting of
quadratic curvature invariants on the Einstein-Hilbert action is considered and
exact vacuum solutions of these quadratic gravities are studied in arbitrary
dimension. We investigate classes of Einstein spacetimes and spacetimes with a
null radiation term in the Ricci tensor satisfying the vacuum field equations
of quadratic gravity and provide examples of these metrics.
