The subject of study is University. The aim is to analyze the existing most common classifications of the University and develop a model of its genetic typology. The method is based on a categorical-system approach using the categorical method «A Number of Information Criteria» (AIC). This article discusses the problems of classification of universities caused by imperfection of methodology. The paper gives a brief overview of the most common classifications of the University, found in the works of Russian and foreign researchers, studied in detail the most representative of them. The article also critically analyzes the concepts used by researchers to classify universities. The paper examines the classification criteria underlying the systematization of universities. It is shown that none of the existing classifications is correct and justified, does not reflect the system of universities and does not allow to cover all their existing types. The article also substantiates the application of the categorical-system approach as a methodology for systematization of the species diversity of universities. The paper proposes the application of a categorical-system approach using the categorical method «A Number of Information Criteria» as a methodology for systematization of the species diversity of universities, on the basis of which the genetic typology of universities is developed. The article considers a number of information criteria reflecting the basic processes, the carriers of which are structural units (components) of the University, such as production, provision, service, consumption, research, export, self-education. A model of genetic typology of the University was developed. It is concluded that after the formation of new and more complex characteristics of a system object, such as a University, its systemic and organizational complexity increases. The obtained model of genetic topology of the University serves as a basis for the development of conceptual, structural, functional, target and evolutionary aspects of the subject area under study, as well as contribute to the development of the scientific theory of the University.