Group theory

In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right.

Quotes

 * Group theory is the mathematical expression of symmetry, providing appropriate mathematical tools for the implementation of symmetry considerations in theoretical physics.
 * The introduction of the digit 0 or the group concept was general nonsense too, and mathematics was more or less stagnating for thousands of years because nobody was around to take such childish steps...-Alexander Grothendieck
 * R. Brown and T. Porter,Analogy, concepts and methodology, in mathematics(chapter_1) Link
 * R. Brown and T. Porter,Analogy, concepts and methodology, in mathematics(chapter_1) Link