  We discuss the geometry of timelike surfaces (two-dimensional submanifolds)
in a Lorentzian manifold and its interpretation in terms of general relativity.
A classification of such surfaces is presented which distinguishes four cases
of special algebraic properties of the second fundamental form from the generic
case. In the physical interpretation a timelike surface can be viewed as the
worldsheet of a ``track'', and timelike curves in this surface can be viewed as
the worldlines of observers who are bound to the track, like someone sitting in
a roller-coaster car. With this interpretation, our classification turns out to
be closely related to (i) the visual appearance of the track, (ii) gyroscopic
transport along the track, and (iii) inertial forces perpendicular to the
track. We illustrate our general results with timelike surfaces in the
Kerr-Newman spacetime.
