This Doctoral Thesis describes the conceptual method of data bank design which
is determined as an approach to develop, apply and manage the databases and
metadata bases. This approach covers the accommodations to the variable problem
domain and its representation, e.g., by increasing/decreasing the level of details
being described. The topics concerning the management of databases and meta\-data
bases deal with an integration of data objects, metadata objects and programs.
A unified computational environment preserves the extensibility of data object
model. The representations of data and metadata are specified by the variety
of data and metadata objects which are embedded into a computational framework.
The design procedure is based on a choice of multilevel conceptualization to capture the semantic features of data/metadata interconnections. The variety of data and metadata objects can be expanded without violation of the computational environment properties.
All the topics give a conceptual framework for thinking about computations with the objects. Several areas of theoretical computer science are covered, including type free and typed $\lambda$-calculus and combinatory logic with applications, evaluation of expressions, computations in a category. The topics, covered in this Thesis accumulated much experience in teaching these subjects in postgraduate computer science courses.