  Introductory courses on quantum mechanics usually include lectures on
uncertainty relations, typically the inequality derived by Robertson and,
perhaps, other statements. For the benefit of the lecturers, we present a
unified approach -- well suited for undergraduate teaching -- for deriving all
standard uncertainty relations: those for products of variances by Kennard,
Robertson, and Schr\"odinger, as well as those for sums of variances by Maccone
and Pati. We also give a brief review of the early history of this topic and
try to answer why the use of variances for quantifying uncertainty is so
widespread, while alternatives are available that can be more natural and more
fitting.
  It is common to regard the states that saturate the Robertson inequality as
"minimum uncertainty states" although they do not minimize the variance of one
observable, given the variance of another, incompatible observable. The states
that achieve this objective are different and can be found systematically.
