VIAM was founded in 1968. In 1978 it was named after its founder, first director and scientific leader, Academician Ilia Vekua. The main direction of VIAM activities:

The investigation of multi-dimensional differential and integral equations and development of methods of their solutions for the problems of shell theory, theory of elasticity, meteorology and radiation transfer theory ( Since 1968 up to now),

The investigations of probability theory and mathematical statistics and their applications to problems of dynamic programming, mass service and processing of experimental data (in 1968–1971);

Development of theoretical and applied problems of programming, including the formation of the system of algorithms and programs to solve the typical problems on the computer ( since 1968 up to now);

Development and application of methods of applied mathematics and computer techniques in organazing the teaching process at higher schools (since 1968 up to now) .

Since the very first days of its foundation VIAM has been establishing scientific contacts (on the basis of bilateral and multi-lateral agreements) with mathematical departments of Lomonosov State University of Moscow, Novosibirsk State University, Kiev State University, Friedrich Shiller University of Iena, Ian Amos Komenski University of Bratislava, Lodz University, Martin Luther University of Halle, University of Rome "La Sapienza", as well as with V. Steclov mathematical Institute of Moscow, M. Keldysh Applied Mathematics Institute of Moscow, I. Curchatov Atomic Energy Institute of Moscow, INRIA. Source: www.viam.hepi.edu.ge