You have a Langenhan Military Model. They also made a little .25 cal. for commercial sale, but the one you have is a .32 which was only made during WWI for sale to the military. While described as a secondary issue, it was more likely an officers pistol, given the fashion of the day for officers to carry small pistols.
The .32 Langenhan can be dangerous if fired with a loose breach block screw. This screw is located in back of the slide and it should be quite tight to be sure the stirrup breach block lock is kept in place (the part with slide grasping grooves in it). If loose, a few shots could cause the stirrup lock to fly up releasing the breach block to fly into your face. (see GERMAN PISTOLS AND REVOLVERS, 1871 - 1945 by Ian V. Hogg.)
I have seen a few of these with cracks in the stirrup shaped breach block lock. For this reason, the stirrup should be checked for cracks prior to use.
Otherwise, it is an interesting historical WWI pistol. The one you have has plenty of blue and looks like an extra nice example. These are not seen as often as they used to be.