The intensification of competition in the market of scientific and educational services forces universities (higher education institutions in general) to search for tools and methods of forming and strengthening their competitive advantages. Practice shows that universities use marketing methods and tools that have proven their effectiveness in various areas of commercial and non-commercial areas. Branding is one of the most effective tools for forming and strengthening unique competitive advantages of universities in the market of scientific and educational services. Consequently, there arises the necessity of building an effective branding system for formation and implementation of universities’ competitive advantages in the market of scientific and educational services. The article develops principles and approaches to the purposeful brand management of the modern university for formation of its competitive advantages. The formation and strengthening of the brand of a modern university is offered by complying its actual characteristics to brand strength criteria. Based on the university’ field, its brand power/strength can be adequately assessed according to the Interbrand criteria. The main ways to ensure compliance of the actual brand characteristics with the defined criteria are investigated and systematized according to the scientific and educational components of the university’ activity. A system of tools for creation a powerful university brand has been formed. Peculiarities of application of marketing methods and tools for extensive support of the university brand in the market of scientific and educational services are highlighted. The circle of representatives of the university top management and also its structural divisions which are involved in brand management is outlined. The scheme of their interaction and distribution of basic administrative functions between them is developed. The obtained results deepen the branding theoretical and methodological principles in terms of forming a purposeful and effective university’s brand management as a market-oriented tool to ensure its competitive advantages in domestic and foreign markets of scientific and educational services. Further research should be aimed at forming a methodological framework for the university’s brand management by formalized procedures.