  We study the effect of global topology of the spatial geometry on the cosmic
microwave background (CMB) for closed flat and closed hyperbolic models in
which the spatial hypersurface is multiply connected. If the CMB temperature
fluctuations were entirely produced at the last scattering, then the
large-angle fluctuations would be much suppressed in comparison with the simply
connected counterparts which is at variance with the observational data.
However, as we shall show in this thesis, for low matter density models the
observational constraints are less stringent since a large amount of
large-angle fluctuations could be produced at late times. On the other hand, a
slight suppression in large-angle temperature correlations in such models
explains rather naturally the observed anomalously low quadrupole which is
incompatible with the prediction of the "standard"
Friedmann-Robertson-Walker-Lemaitre models. Interestingly, moreover, the
development in the astronomical observation technology has made it possible to
directly explore the imprint of the non-trivial topology by looking for
identical objects so called "ghosts" in wide separated directions. For the CMB
temperature fluctuations identical patterns would appear on a pair of circles
in the sky. Another interesting feature is the non-Gaussianity in the
temperature fluctuations. Inhomogeneous and anisotropic Gaussian fluctuations
for a particular choice of position and orientation are regarded as
non-Gaussian fluctuations for a homogeneous and isotropic ensemble.
