The Gelfand-Kirillov dimension is a concept in mathematics, particularly in the field of representation theory and algebra. It measures the growth rate of the dimensions of the spaces of representations of an algebra or a group. Specifically, it helps classify algebras based on how their representations behave as the degree of the representation increases. This dimension is named after mathematicians I. Gelfand and A. Kirillov, who introduced it to study the properties of certain algebras. A higher Gelfand-Kirillov dimension indicates more complex growth, while a dimension of zero suggests a more straightforward structure. This concept is useful in understanding the underlying properties of various mathematical objects.