  The theory of cosmological perturbations is the main tool which connects
theories of the early universe (based on new fundamental physics such as string
theory) with cosmological observations. In these lectures, I will provide an
introduction to this theory, beginning with an overview of the Newtonian theory
of fluctuations, moving on to the analysis of fluctuations in the realm of
classical general relativity, and culminating with a discussion of the quantum
theory of cosmological perturbations. I will illustrate the formalism with
applications to inflationary cosmology. I will review the basics of
inflationary cosmology and discuss why - through the evolution of fluctuations
- inflation may provide a way of observationally testing Planck-scale physics.
