  The underlying mathematical structures of gauge theories are known to be
geometrical in nature and the local and global features of this geometry have
been studied for a long time in mathematics under the name of fibre bundles. It
is now understood that the global properties of gauge theories can have a
profound influence on physics. For example, instantons and monopoles are both
consequences of properties of geometry in the large, and the former can lead
to, e.g., CP-violation, while the latter can lead to such remarkable results as
the creation of fermions out of bosons. Some familiarity with global
differential geometry and fibre bundles seems therefore very desirable to a
physicist who works with gauge theories. One of the purposes of the present
work is to introduce the physicist to these disciplines using simple examples.
