  The theory of cosmological perturbations has become a cornerstone of modern
quantitative cosmology since it is the framework which provides the link
between the models of the very early Universe such as the inflationary Universe
scenario (which yield causal mechanisms for the generation of fluctuations) and
the wealth of recent high-precision observational data. In these lectures, I
provide an overview of the classical and quantum theory of cosmological
fluctuations. Crucial points in both the current inflationary paradigm of the
early Universe and in some proposed alternatives are that, first, the
perturbations are generated on microscopic scales as quantum vacuum
fluctuations, and, second, that via an accelerated expansion of the background
geometry (or by a contraction of the background), the wavelengths of the
fluctuations become much larger than the Hubble radius for a long period of
cosmic evolution. Hence, both Quantum Mechanics and General Relativity are
required in order to understand the generation and evolution of fluctuations.
  After a review of the Newtonian theory of perturbations, I discuss first the
classical relativistic theory of fluctuations, and then their quantization.
Briefly summarized are two new applications of the theory of cosmological
fluctuations: the trans-Planckian ``problem'' of inflationary cosmology and the
study of the back-reaction of cosmological fluctuations on the background
space-time geometry.

High Energy Physics - Theory;Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology