The set of whole numbers less than and coprime to n, with the operation of multiplication modulo n, forms an Abelian group (try to prove it for yourselves). We'll write Mn for this group, and call all such groups modulo groups or M-groups. M-groups are easy to compute. It is also particularly easy to calculate quotient groups of M-groups, making them a good source of examples and practice for the beginner. There are also some very hard, possibly unsolved, problems in classifying M-groups. In attacking such problems there is an interaction between number theoretical and group theoretical arguments which makes this a rich topic, for projects or personal pleasure.