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MQFT is a biennially held international conference this year dedicated to the 82nd anniversary of professor Alexander Nikolaevich Vasiliev (1940-2006) and 80th anniversary of professor Vladimir Dmitrievich Lyakhovsky (1942-2020). From year to year, the conference attracts the most distinguished members of the world-famous centres for theoretical physics. The main topics of the conference are related to the most actual and important problems related to the construction and investigation of the quantum field theory models. During the conference, it is proposed to discuss the modern methods of QFT and applications of these methods to the elementary particle physics and statistical physics, gravitation and cosmology, mathematical problems and methods in quantum field theory, and integrable models. During the conferences, the special importance is placed upon the methods and approaches created and developed by the researchers of “Vasiliev scientific school”, the school of theoretical physics that was established by Alexander Nikolaevich Vasiliev and has since then aquired an international scope. Currently, as many as 10 professors and 20 Ph.D. researchers belong to the school. Their successful work in the field of theoretical physics is conducted either in Russia or around the world, many of them have developed their own methods and approaches and acquired many students of their own. Results obtained by A.N.Vasiliev and his followers revealed the deep intrinsic affinity between classical complex systems with many degrees of freedom and quantum objects, which allowed to apply successfully the powerful mathematical methods of the quantum field theory to the phenomena of seemingly completely different nature. This year the conference will include an extended section on the mathematical foundations of quantum field theory that is dedicated to the 80th anniversary of professor Vladimir Dmitrievich Lyakhovsky (1942-2020), who was a close friend of Alexander Nikolaevich Vasiliev and the organizer of the first MQFT conferences. In this section we welcome contributions that are related to the scientific interests of Vladimir Dmitrievich: representation theory, symmetries in QFT, quantum integrable systems, quantum groups.