On the sovereignty of the several states, I would add that while the states may, by Constitutional operation, effectively dissolve and rebuild the central government from the ground up, the reverse is not true; the federal government has no mechanism by which to dissolve a state, to kick it out, or anything else. Obdigore nailed the description, but I would qualify that the "highest is rightest" principle for the relationship between the federal and state governments is (unlike between state and local governments) explicitly limited to those specific areas that the Constitution empowers the federal government to act.