  This is a PhD thesis in low-dimensional topology.
  Its main purpose is to examine so-called t\^ete-\`a-t\^ete twists. Those were
defined by A'Campo and give an easy combinatorial description of certain
mapping classes on surfaces with boundary. Whereas the well-known Dehn twists
are twists around a simple closed curve, t\^ete-\`a-t\^ete twists are twists
around a graph. It is shown that t\^ete-\`a-t\^ete twists describe all the
(freely) periodic mapping classes. This leads, among other things, to a
stronger version of Wiman's 4g+2 theorem from 1895 for surfaces with boundary.
  On closed surfaces, some t\^ete-\`a-t\^ete twists can be used to generate the
mapping class group.
  Another main result is a simple criterion to decide whether a Seifert surface
of a link is a fibre surface. This gives a short topological proof of the fact
that a Murasugi is fibred if and only if its two summands are.
