- differential geometry: smooth manifolds and submanifolds endowed with different structures, their geometry and applications in general theory of relativity; geometry and topology of fiber bundles; Osserman manifolds; representations of groups on spaces of curvature tensors; homogenous and symmetric spaces; Lie groups and algebras; special holonomies; small geodesic balls; Chen's curvature invariants; quantum groups and their applications; knot and link theory;
- mathematical physics: quantum and classical models on p-adic, adelic and non-commutative spaces,
- probability and statistics: stochastic, stationary and stable processes; Brownian motion; probabilistic and other methods in combinatorics;
- visual mathematics and computing geometry, visualization of geometrical results in education; connection between empirical and theoretical knowledge in computer assisted teaching of geometry; construction and application of software LinKnot in knot theory.

This field is naturally intertwined with other fields of mathematics: Lie groups, quantum groups, global analysis, topology, non-commutative geometry, theory of gravitation and theory of relativity, etc.

Results of differential geometry are used, for instance, in statistics (geometries of small geodesic spheres and tubes), architecture (minimal surfaces) and civil engineering (deformations of surfaces), genetic engineering.

Research in the field of p-adic, adelic, and non-commutative geometry belong to a new and actual field of contemporary mathematical physics. Their importance is in the investigations non-Archimedean and non-commutative properties of space-time geometry and quantum phenomena on very small distances. It is the continuation of a successful research of MNTR project (2002-2005), 1426 'Quantum models on non-commutative and adelic spaces'.

Investigations in the fields of stochastic processes, Brownian motion and etc., are today of the great importance since they are applicable in combinatorics, physics, insurance and financial mathematics, etc.

Computer graphics is one of the most important computer fields and it cannot be imagined without the use of differential geometry of curves and surfaces, as well as the application of required numerical methods.

The problem of visualization and animation is one of the most interesting current problems in the computer science, which renders the interdisciplinary approach to this field indispensable.

The great project of the European Union, established by the Bologna Declaration, devotes special attention to education in the field of geometry by using information technologies.

In that period, starting from the initial phase, we managed to attain a high level of development in differential geometry which resulted in a larger number of works published in international journals. Several scientific international and national meetings were organized by the members of this project, such are:

- international meetings in the fields of
- geometry (International Conference on Differential geometry and its Applications, 1988, Contemporary geometry and related topics, 2002, 2005),
- visualizations (annual meetings of DAAD project 'Multimedia Technology for Mathematics and Computer Science Education': 2004, 2005),
- mathematical physics (Summer Schools of Modern Mathematical Physics, 2001, 2002, 2004, and 2nd International Conference on p-adic Mathematical Physics, 2005),

- national meetings (very often with international participants) in the
filed of
- geometry (Geometrical Seminars, 1980-2004, totally fourteen meetings).

The proceedings of many of those meetings were published, some of them by
the world-wide known publishing companies such are World
Scientific,
American
Institute of Physics, etc.

Actuality and scientific value of those projects, in the previous period,
has been confirmed by institutional and personal contacts with eminent
institution and individuals. International cooperation was developed, with
participation in international projects, financed by German foundation DAAD.
We emphasize only the institutional cooperation with:

- Technical University, Berlin,
- Free University, Berlin
- Moscow State University-Chair of Differential Geometry and Applications,
- Zusse Institute, Berlin,
- Tor Vergata University, Rome
- Pavle Savić, French-Serbian bilateral cooperation,
- Steklov Mathematical Institute, Moscow,
- Abdus Salam International Centre for Theoretical Physics, Trieste.