Cosmological perturbation theory (CPT) is an important tool with which inhomogeneities that seed the observed structure of our universe can be studied. This thesis introduces the subject of CPT and discusses applications of this at both linear and second order. At linear order the evolution of the curvature perturbation around horizon crossing is examined. We study single field inflation models numerically, and compare the curvature perturbation at horizon crossing to that at the end of inflation. In addition, linear-order CPT is extended to the case of a multi-fluid system and an approximation for the velocities of the baryons and photons in the early universe as well as the strength of the electric field is found. We use second order CPT to study magnetogenesis. By using fully relativistic, non-linear CPT we show how magnetic fields are generated. This is done by presenting the first fully analytical calculation of the magnetic field at second order. Our results suggest that magnetic fields with strengths of the order of 10²⁷G and with scale dependence M ∝ k⁴ may be generated - findings which are largely in agreement with previous numerical results. We end by outlining possible extensions to this work, in particular related to the study of primordial magnetogenesis.