I heard that at that time when Kosovo was granted independence the Russia's side said that it was a violation of the international law. How was it a violation? Which points of the law were violated?
NATO used force, or the threat of force, to remove Kosovo from Serbia.
The UN charter, Article 2, paragraph 4:
All Members shall refrain in their international relations from the threat or use of force against the territorial integrity or political independence of any state, or in any other manner inconsistent with the Purposes of the United Nations.