  This tutorial, addressing physics teachers and undergraduate students, aims
at clarifying some aspects of time in special relativity. In particular, time
dilation is usually presented only as the well-known ratio of lab time over
proper time, $R$. Above ratio is useful, e.g. for describing the decay length
of an unstable particle in the lab. But essential characteristics of time
dilation, missed out in many textbooks, are manifest in the differences
(quadratic, absolute and relative) between lab time and proper time.
  After an introduction to the basics, we regard the movement of a clock over a
fixed spatial distance $\Delta x$. Explicit formulae are given for $R$ and for
the differences, and their behaviour as functions of the velocity is discussed
and plotted. Approximate formulae are given for very slow movements. Time
synchronization within an inertial system by "slowly" moving a clock over a
finite distance $\Delta x$, mentioned vaguely in some textbooks, may
quantitatively be comprehended by requiring the time difference to be less than
the clock's time resolution. We derive explicit formulae for the maximal
velocity obeying these constraints (to the best of our knowledge not presented
elsewhere).
