  In this thesis we investigate the stationary properties and formation process
of a class of nontopological solitons, namely Q-balls. We explore both the
quantum-mechanical and classical stability of Q-balls that appear in
polynomial, gravity-mediated and gauge-mediated potentials. By presenting our
detailed analytic and numerical results, we show that absolutely stable
non-thermal Q-balls may exist in any kinds of the above potentials. The latter
two types of potentials are motivated by Affleck-Dine baryogenesis, which is
one of the best candidate theories to solve the present baryon asymmetry. By
including quantum corrections in the scalar potentials, a naturally formed
condensate in a post-inflationary era can be classically unstable and fragment
into Q-balls that can be long-lived or decay into the usual baryons/leptons as
well as the lightest supersymmeric particles. This scenario naturally provides
the baryon asymmetry and the similarity of the energy density between baryons
and dark matter in the Universe. Introducing detailed lattice simulations, we
argue that the formation, thermalisation and stability of these Q-balls depend
on the properties of models involved with supersymmetry breaking.
