  The three key documents for study geometry are: 1) "The Elements" of Euclid,
2) the lecture by B. Riemann at G\"ottingen in 1854 entitled "\"Uber die
Hypothesen welche der Geometrie zu Grunde liegen" (On the hypotheses which
underlie geometry) and 3) the "Erlangen Program", a document written by F.
Klein (1872) on his income as professor at the Faculty of Philosophy and the
Senate of the Erlangen University. The latter document F. Klein introduces the
concept of group as a tool to study geometry. The concept of a group of
transformations of space was known at the time. The purpose of this informative
paper is to show a relationship between geometry and algebra through an
example, the projective plane. Erlangen program until today continues being a
guideline of how to study geometry.
