A simple and powerful new method for the treatment of spin wave interactions is introduced and used toobtain the corrections to the energy and magnetization of ferromagnets, antiferromagnets and ferrimagnets.The results previously obtained by Dyson and by Oguchi using complicated analysis are reproduced andextended by means of elementary considerations which throw light on the physical interpretation of thecorrections. In the case of a ferromagnet the validity of the random phase approximation is discussed, andthe properties of the continuous medium model are calculated: in particular, the spin wave exchange-collisioncross section is obtained in a simple way.