Changes in the various fields of knowledge influenced the pedagogical science. The article explains the structure of the foundations of modern pedagogy through paradigmal and methodological aspects. Bases of modern pedagogy include complex of paradigms, object and subject of science, general and specific principles, methods and technologies. Paradigmal analysis of bases of modern pedagogy showed that paradigms performed informational, instrumental and technological functions through connections with factors, approaches and principles accordingly. The research of methodological aspect of bases of modern pedagogics allowed to define the structure of the methodological system and main characteristics of the pedagogical system. In the article considers specific principles of optimality, optimization, adaptation and rules of their use in a pedagogical theory and practice.