An algebraic structure is a set with operations between its elements that follow certain rules. As an example of such a structure consider the integers and the operation ’ \(+\) ’. What are the properties of this addition? Already in elementary school one learns that the sum \(a+b\) of two integers a and b is another integer. Moreover, there is a number 0 such that \(0+a=a\) for every integer a, and for every integer a there exists an integer \(-a\) such that \((-a)+a=0\) . The analysis of the properties of such concrete examples leads to definitions of abstract concepts that are built on a few simple axioms. For the integers and the operation addition, this leads to the algebraic structure of a group, which is the starting point in this chapter.