Abstract
The aim of this paper is further development of the mathematical theory of algorithmic complexity measures for evaluation of the computer software design and utilization. We consider some basic concepts and constructions from the theory of algorithmic complexity and develop a system structure in the theory of algorithmic complexity. The paper contains main concepts from the axiomatic complexity theory, which are fundamental for the whole theory of algorithmic complexity. Important classes of dual complexity measures are studied. The research is oriented at the development of software engineering and, in particular, creation of more efficient software metrics.