Our research was focused on the development of more efficient algorithms as well as their application to various fields of information technology. The basic research included solving NP-hard combinatorial optimization problems (e.g. the facility location problem and the data replication problem) with approximate, randomized, and other heuristic methods; solving network routing problems (e.g. a dynamic routing algorithms and permutation routing algorithms in networks with the topology of circulant graphs); the design of modern compiling techniques (e.g. the design of a new combined LL and LR parsing algorithms); the design of window functions and the use of recursive systems in various digital signal processing algorithms; the design of improved algorithms for integer polynomial minimax approximation and Viterbi algorithm; the analysis of schemes of XML and their relation to databases. The application oriented research included the design and application of digital filters in various telecommunication devices; improvement of certain measuring instruments such as spectral analysers; superscalar, multithreaded, and other advanced computer architectures; debugging techniques for lazy program execution; approximation algorithms to obtain robust solutions of certain combinatorial optimization problems such as the location problem; application of optimal integer solutions of certain problems in relational data-base design; routing algorithms in circulant computer networks; combined improvement of audio/video compression in multimedia systems; the design of information systems; improvements in software process management; software metrics; software quality measurement, and data quality measurement. To summarize, the aims of our research program were in the development and application of new, better algorithms, techniques, and methods that can be used to solve several real problems that appear in various topical areas of IT. Although fundamental research may, at first glance, appear theoretical, it is this formality and generality that offers and/or improves the applicability of the solutions (algorithms, techniques, methods). This is proved by algorithms that have originally been developed for a specific problem in a given area (e.g. digital signal processing), but have later efficiently been applieddue to general theoretical treatment in other areas (e.g. information system development).