What were the goals of the UN? What is its main principle different from the pre-war League of Nations?

After World War II, an institution was created to regulate relations between states in broad areas. The UN has become one of the main bodies for coordinating the work of states. Initially, there were about fifty countries in it, but after several decades their number increased by about 4 times. The UN differed from the League of Nations in that it was in charge not only of issues of war and peace. Also, this organization was based on the equality of participants with the absence of infringements of the losing countries.