The object of the study are the intelligent adaptive hypermedia computer-based training systems with matching personal abilities of the user. The purpose of the study is the development of models and methods for constructing intelligent adaptive hypermedia systems, which through the usage of personal abilities of the user, and contribute to the intensification of the process of improving the quality of computer-based training. Methods of the research area complex of mathematical modelling, a set theory, and the theory of intelligence; algebra predicates and predicate operations for the formalization of knowledge, descriptions of management models and modelling adaptation of learning strategies; a comparator method of identification describes the intelligent features of adaptive hypermedia systems. The equipment is a personal computer. Theoretical and practical results of the study were realized in the creation of new methods and models of building intelligent adaptive hypermedia system based on the use of the personal abilities of the user, the application of the developed models and computer-based training technology has allowed practiced learning model (in the form of training programs, adaptive e-learning) using the navigation rules on the level of software automate the process of adaptation of learning through concealing ties, which implements a set of procedures and the generation of dynamic modification of the strategy presentation of educational material. Scientific novelty of the research is the first time usage of a method of training and updating knowledge in intelligent tutoring systems, information, which comprises the steps of perception of the standard of knowledge, formation, reproduction and comparison of subjective image with the standard of knowledge that can increase the intensity and effectiveness of computer-based training, the first time usage of a model of learning based on navigation rules generation and dynamic modification of learning strategies in the basis of the algebra of finite predicates, which simplifies the process of learning through the use of a unified formal representation of knowledge and learning strategies, improved multi-level model of the organization hypermedia space in which, unlike the existing ones, the notion of teaching predicates, which allowed a single representation of the educational space in the basis of the algebra of finite predicates and predicate operations, received further development an adaptive model of the user thanks to the introduction of tolerance factor of knowledge, allowing to individualize the learning process in accordance with the level of knowledge of the user. The results of the dissertation research found practical application in the construction of intelligent system created to improve the skills of technical staff OSP "Plant" Svitlo Shakhtarya" (Kharkiv). The proposed improvement soft aching methods used at the Department of Software Engineering Kharkiv National University of Radio Electronics in teaching special subjects "Multimedia Systems", "Multimedia and Internet Virtuality" and at the Department of Intelligent Computer Systems of the National Technical University "Kharkiv Polytechnic Institute" in the teaching of subjects "Information resource providing linguistic activity", "Automated processing of natural language". Scientific and practical results of the thesis can be used in organizations working with development, research, implementation and operation of intelligent tutoring systems, systems identification and modelling of human intellectual activity, as well as in the educational process in the preparation of specialists in the areas of "Software Engineering", "Engineering of software".