  An idea to present a classical Lie group of positive dimension by generators
and relations sounds dubious, but happens to be fruitful. The isometry groups
of classical geometries admit elegant and useful presentations by generators
and relations closely related to geometry. They allow to make fast and
efficient geometric calculations. In this paper simple presentations of the
isometry groups of Euclidean plane, 2-sphere, the real projective plane and
groups SO(3), O(n) are introduced.
