  When a charged particle travels across the vacuum chamber of an accelerator,
it induces electromagnetic fields, which are left mainly behind the generating
particle. These electromagnetic fields act back on the beam and influence its
motion. Such an interaction of the beam with its surro undings results in beam
energy losses, alters the shape of the bunches, and shifts the betatron and
synchrotron frequencies. At high beam current the fields can even lead to
instabilities, thus limiting the performance of the accelerator in terms of
beam quality and current intensity. We discuss in this lecture the general
features of the electromagnetic fields, introducing the concepts of wakefields
and giving a few simple examples in cylindrical geometry. We then show the
effect of the wakefields on the dynamics of a beam in a linac, dealing in
particular with the beam breakup instability and how to cure it.
