  Anti--de Sitter spacetime is important in general relativity and modern field
theory. We review its geometrical features and properties of light signals and
free particles moving in it. Applying only elementary tools of tensor calculus
we derive \textit{ab initio\/} all these properties and show that they are
really weird. One finds superluminal velocities of light and particles,
infinite particle energy necessary to escape at infinite distance and spacetime
regions inaccessible by a free fall, though reachable by an accelerated
spaceship. Radial timelike geodesics are identical to the circular ones and
actually all timelike geodesics are identical to one circle in a fictitious
five--dimensional space. Employing the latter space one is able to explain
these bizarre features of anti--de Sitter spacetime; in this sense the
spacetime is not self--contained. This is not a physical world.
