  In this thesis we consider several aspects of general relativity relating to
exact solutions of the Einstein equations. In the first part gravitational
plane waves in the Rosen form are investigated, and we develop a formalism for
writing down any arbitrary polarisation in this form. In addition to this we
have extended this algorithm to an arbitrary number of dimensions, and have
written down an explicit solution for a circularly polarized Rosen wave. In the
second part a particular, ultra-local limit along an arbitrary timelike
geodesic in any spacetime is constructed, in close analogy with the well-known
lightlike Penrose limit. This limit results in a Bianchi type I spacetime. The
properties of these spacetimes are examined in the context of this limit,
including the Einstein equations, stress-energy conservation and Raychaudhuri
equation. Furthermore the conditions for the Bianchi type I spacetime to be
diagonal are explicitly set forward, and the effect of the limit on the matter
content of a spacetime are examined.
