Landau’s book “**Symmetry**” explains it as follow:

**Automorphism** = Congruence= 叠合 has

1). **Proper** 真叠合 (symmetry: left= left, right = right)

2). **Improper** 非真叠合 (non-symmetry: reflection: left changed to right, vice-versa).

Congruence => **preserve** size / length

=> Movement 运动 (translation 平移, rotation about O )

= Proper congruence (Symmetry)

In Space S, the Automorphism that preserves the structure of S forms a Group **Aut(G)**.

=> **Group Aut(G) describes the Symmetry of Space S.**

Hence Group is the language to describe Symmetry.