  In this thesis we investigate several aspects related to the theory of
fluctuations in the Cosmic Microwave Background. We develop a new algorithm to
calculate the angular power spectrum of the anisotropies which is two orders of
magnitude faster than the standard Boltzmann hierarchy approach (Chapter 3).
The new algorithm will become essential when comparing the observational
results of the next generation of CMB experiments with theoretical predictions.
The parameter space of the models is so large that an exhaustive exploration to
find the best fit model will only be feasible with this new type of algorithm.
We also investigate the polarization properties of the CMB field. We develop a
new formalism to describe the statistics of the polarization variables that
takes into account their spin two nature (Chapter 2). In Chapter 4 we explore
several physical effects that create distinct features in the polarization
power spectrum. We study the signature of the reionization of the universe and
a stochastic background of gravitational waves. We also describe how the
polarization correlation functions can be used to test the causal structure of
the universe. Finally in Chapter 5 we quantify the amount of information the
next generation of satellites can obtain by measuring both temperature and
polarization anisotropies. We calculate the expected error bars on the
cosmological parameters for the specifications of the MAP and Planck satellite
missions.
