IMCS/

- Theoretical foundations of computer science (formal models of computation, grammars and formal languages, computational algebra);
- Natural language processing;
- Modeling and simulation systems;
- Software development technology (methods, advanced design environments for programming systems development, methodologies and integrated technologies for software development, unstructured data processing systems).

- Algebra (theory of radicals, structural problems in algebraic systems near to rings, modules and algebras);
- Quasigroups and combinatorial analysis (general theory of quasigroups and algebraic operations, combinatorial problems in quasigroups and applications in coding theory and cryptology);
- Mathematical logic (algorithmic problems of functional expressibility as well as its generalizations in non-classical logics);
- Topological algebra;
- Geometry of discrete groups.

- Mathematical modeling;
- Numerical methods;
- Probability theory;
- Game theory and optimal control;
- Modeling of economic processes.

Theoretical and applied research in information systems domain (Theoretical research: new algorithms and technologies for knowledge acquisition, formalization and management; processing of ultrasound images. Applied research: decision support systems, intelligent e-learning and e-training systems, Web content management systems). Information society creation.

- Qualitative theory of differential equations and theory of algebraic invariants;
- Application of group analysis and Lie algebras for studying of differential equations;
- Functional analysis and complex normal functions.