  This paper is an extended abstract of the dissertation presented by the
author for the doctoral degree in physics and mathematics (in Russia). The main
characteristic studied in the dissertation is combinatorial complexity, which
is a "counting" function associated with a language and returning the number of
words of given length in this language. For several classes of languages, a
variety of problems about combinatorial complexity and its connections to other
parameters of languages are studied. A brief introduction to the topic and the
formulations of results are presented. No proofs are given; instead, the papers
containing the proofs are cited.
