  The Alcubierre warp spacetime yields a fascinating chance for comfortable
interstellar travel between arbitrary distant places without the time dilation
effect as in special relativistic flights. Even though the warp spacetime needs
exotic matter for its construction and is thus far from being physically
feasible, it offers a rich playground for studying geodesics in the general
theory of relativity. This paper is addressed to graduate students who have
finished a first course in general relativity to give them a deeper inside in
the calculation of non-affinely parametrized null and time-like geodesics and a
straightforward approach to determine the gravitational lensing effect due to
curved spacetime by means of the Jacobi equation. Both topics are necessary for
a thorough discussion of the visual effects as observed by a traveller inside
the warp bubble or a person looking from outside. The visual effects of the
traveller can be reproduced with an interactive Java application.
