What system of government does the United States of America operate?
The government of the USA is federal government of the republic of fifty states, containing one capital district and several other territories, which constitute the United States.
Federal government is a set of three main branches: legislative, executive and judicial. The powers of branches, according to the Constitution of the United Stated, are assigned to the President, the Congress and the federal courts. Acts of the US Congress restrict and control the powers of the branches.
The full official name of the republic is "United States of America". It's the only name appearing on money, treaties and all the legal cases it takes part in.
There are several federal republics in the today's world, including the Russian Federation, Germany, Brazil, Austria and others. The types of their subdivision are different: federal subjects, provinces, states etc.