The book is a study of some philosophical and epistemological problems of cosmology. The philosophical positions of the classics of cosmology of the 20th century are analyzed (A. A. Friedman et al . ), as well as a number of prominent modern cosmologists. Cosmology is not at all one of the "ironic sciences" as it is sometimes depicted. Physical reality in cosmology manifests itself as a fixation of the results of the interaction of the observer with the object under study (carried out through the means and conditions of cognition) expressed in the language of science. The meaning of this concept in the context of this type of scientific rationality is revealed by the true theory. It is shown that cosmology, in fact, is moving from traditional methods of research to non-traditional, t. e. changes are made in its foundations, imposed by new types of studied objects. The need for a radical change in the meanings of traditional concepts in cosmology, such as space, time, infinity The conditions and limits of their applicability within the framework of new cosmological theories. are analyzed. Particular attention is paid to new fundamental concepts that have appeared in cosmology in recent years: Multiverse (Metaverse), cosmological vacuum, dark matter, dark energy, accelerated expansion of the Universe, etc. On some issues that are at the forefront of modern cosmology, there is a discussion between the authors of the book. An attempt is made to show the heuristic role of philosophy in understanding these problems. The book is designed for philosophers, cosmologists and everyone interested in the philosophical problems of modern science.