The article addresses issues related to the effective organization of the educational process in postgraduate pedagogical institutions through the use Information and Communication Technologies (ICT), specifically exemplified by LMS Moodle. The possibilities LMS for creating a learning environment that meets the requirements of high-quality postgraduate education for educators are demonstrated. The authors elucidate the role of postgraduate pedagogical education amidst the contemporary transformations of Ukrainian society, emphasizing the necessity for additional knowledge and experience in ICT utilization among educators. Postgraduate education courses facilitate the integration of professional and educational activities of educators, aiming to foster their abilities for self-organization, self-development, and independent acquisition of constantly evolving information, enabling them quickly adapt to changes in the socio-economic environment. The substantial flow of information necessitates additional knowledge and experience in using information and communication technologies by educators, thereby imposing new demands on the organization of postgraduate education for teachers. The authors proved that the effective solution to the personalization task in postgraduate education is possible only through the integration of teaching technologies and information and communication technologies. Modern learning management systems have a powerful arsenal of tools for implementing innovative teaching models. This paper analyzes the capabilities of LMS Moodle in terms of course administration, personalized learning, organizing group and individual interactions (Forum, Chat, Choice, Workshop, Wiki, MindMap), monitoring, and analytics of the educational trajectory of each student. Construction of branched course structures (Lesson element), the organization of problem-oriented content with elements of group processing, tracking the interests of each learner through the selection of educational information blocks and feedback (Lesson elements, Assignment, Feedback, Survey), operational monitoring of knowledge quality (Lesson elements, Quiz, Choice), and the organization of the educational process using the flipped classroom model are analyzed. According to the authors, future research prospects may involve the development of new tools to support the learning process in LMS Moodle, particularly related to addressing the complexity of questions to ensure the objectivity of assessing learners' knowledge.