The Third Reich Heer(army) and Luftwaffe(airforce) rank of Hauptmann is equivalent to that of Captain in the current day US Army and US Airforce. It was the third officer rank, above Oberleutnant but below Major.
The Kriegsmarine equivalent of the Hauptmann was called Kapitänleutnant whereas the Waffen-SS equivalent was the SS-Hauptsturmführer.
For a more complete overview
of which ranks existed
, see Wehrmacht ranks
The page that helped me with this writeup is no longer on the internet, but it used to live at www.wehrmacht-association.com/Open_Pages/ranks.htm