The article in the systematic and ordered way presents the most important philosophical problems, which are undertaken with regard to their close connections with contemporary (scientific) cosmology. Lately more and more often the issue mentioned above is called philosophy of cosmology. In the first part of that article, with accordance to the broad understanding of that philosophy, methodological problem of cosmology containing both: its external methodology (general and particular) and so-called internal methodology has been presented. The second part of the article contains various philosophical questions which are undertaken in the context of concrete achievements of contemporary scientific cosmology. They include issues from the field of philosophy of nature, philosophy of God, and ontology.