A presentation of a group is a description of a set and a subset of the free group generated by , written , where (the identity element)
is often written in place of . A group presentation defines the quotient
group of the free group by the normal subgroup
generated by ,
which is the group generated by the generators subject to the relations .

Examples of group presentations include the following.

1. The presentation
defines a group, isomorphic to the dihedral group of finite order , which is the group of symmetries of a regular -gon.