すみません。
英語の文献を全く読んだことがないので、うまく訳出できないんです。
きれいな訳語（完璧でなくても）ができる方、翻訳してください。
よろしくお願いいたします。

Groups form an important tool in the study of geometricalsymmetry.
Many geometrical objects show symmetries of varying kinds and the
natural way to classify them is by means of the groups they admit.
Later we give some examples.
For a fuller discussion we refer to the books by Speiser,Weyl and
Coxeter.

We shall need a formula for the number of orbits in a set.

THEOREM: Let G be a finite group acting on a finite set S.
For each g∈G let c_g be the number of points fixed by g.
Then the number of orbits is

t=1/|G|　X_g∈G c_g