Have to correct a couple of the things said above -
First jet engine? Us
First Turbo prop? Us
First airliner powered by either? Us
First SST? Us
First jet engine - The first jet engine to ever run was made by Professor Ernst Heinkel, in March 1937. It was the hydrogen fuelled Heineken He S 2. The engine only ever ran on a test stand, and its construction was overseen by Hans Joachim Pabst von Ohain.
(Whittle's engine first ran on 12-4-1937, a couple of weeks later than the Heinkel engine)
Whittle, however, holds the first patent for a jet engine.
First turboprop - Not sure of the type, but the Germans made a turboprop in the latter stages of WW2.
First SST - Correct me if I'm wrong, but I thought the Tupolev Tu-144 was earlier than the Concorde?