[AaronInCarolina]

The 1st paragraph is a grant of judicial power, in the aggregate. The 2nd paragraph carves that judicial power into original jurisdiction (which means to try the case), and appellate jurisdiction.

Then that interpretation would mean that ANY case involving a state would go straight to the Supreme Court. Then why are there so few (according to Congressman Billybob). Seems like the SC would be overwhelmed with cases if all cases involving a state go straight to the SC.

[Cboldt]

-- Then that interpretation would mean that ANY case involving a state would go straight to the Supreme Court. Then why are there so few ... --

There are few because SCOTUS and Congress colluded to provide joint original jurisdiction, between SCOTUS and lower courts. SCOTUS has the option to take original jurisdiction in any case in which a state is a party (but see limited subject matter jurisdiction in the 1st paragraph).

Hat tip to Mr Rogers, see http://law.onecle.com/constitution/article-3/32-original-jurisdiction.html