Abstract
In the present paper first a statistical theory of 2-dimensional grain growth for the textureless case based on first principles - the von Neumann - Mullins equation and the topological grain size - grain sides relationship - is described. Then it is shown that the latter relationship follows from two fundamental topological principles, the principles of complete and random surface covering, which are shown to be responsible also for other empirical topological 2-D and 3-D relationships (e.g. Weaire equation). Finally, textures are introduced into the topological discussion.