This is first in a series of blogs that aim to explain the very basics of group theory while capturing its essence. To understand groups one must first understand the notion of symmetries, a symmetry is a mapping from an object to itself that preserves some “structure”. For example lets take a regular polygon, and lets say that the structure a symmetry preserves is distances and angles. Then for a square the symmetries are: The identity mapping which maps every point in the square to itself. Anticlockwise rotations of $90,180, 270$ degrees Relfections about the two diagonals Reflections about the...