  Symmetry-breaking phase transitions are ubiquitous in condensed matter
systems and in quantum field theories. There is also good reason to believe
that they feature in the very early history of the Universe. At many such
transitions topological defects of one kind or another are formed. Because of
their inherent stability, they can have important effects on the subsequent
behaviour of the system. In the first of these lectures I shall review a number
of examples of spontaneous symmetry breaking, many of which will be discussed
in more detail by other lecturers, and discuss their general features. The
second lecture will be mainly devoted to the conditions under which topological
defects can appear and their classification in terms of homotopy groups of the
underlying vacuum manifold. In my final lecture, I will discuss the `cosmology
in the laboratory' experiments which have been done to try to test some of the
ideas thrown up by discussions of defect formation in the early Universe by
looking at analogous processes in condensed-matter systems.
