  In these Lectures a method is described to analyze the effect of quantum
fluctuations on topological defect backgrounds up to the one-loop level. The
method is based on the spectral heat kernel/zeta function regularization
procedure, and it is first applied to various types of kinks arising in several
deformed linear and non-linear sigma models with different numbers of scalar
fields. In the second part, the same conceptual framework is constructed for
the topological solitons of the planar semilocal Abelian Higgs model, built
from a doublet of complex scalar fields and one U(1) gauge field.
