We perform a linear perturbation study of two instances of Bianchi III manifolds: dust and radiation. Two distinct methods are used to ascertain the fate of cosmological perturbations. In the first part we take the metric approach and perturb the metric component by component. Once we construct gauge-invariant variables we work without fixing the gauge and use the perturbations as ingredients in gauge-invariant equations that result when the field equations are enforced to first order. Exact solutions to gauge-invariant equations are extracted explicitly. When possible, we rewrite our solutions as wave equations, giving evidence not only of gravitational radiation, but also sound waves in some instances. When explicit wave equations are not possible, we discuss asymptotic form or give some numerical results.

In the second part we compare our results to those stemming from a covariant approach that relies on identifying covariant physical quantities that vanish in the background. These quantities are gauge-invariant to first order in perturbation theory and thus constitute the ingredients of the study. One such quantity is the comoving fractional density gradient. We make some approximations necessary to decouple the field equations written in terms of these physical variables and discuss the failure of these approximations to yield wave equations or any equations comparable with those of part one.

A brief summary concludes the thesis with an overview of our successes in relation to the two approaches.