Hi Hermit! It appears that you have a Military Mauser and is called strangely enough a "byf 41". The byf is the Ordnance Code for Mauser and it was made in 1941. The serial number, which is located on the frame front, just below the barrel, would be helpful. It will consist of four digits ending in 74, with a script letter below it. It is possible there is no letter.
The magazine is an fxo, not an fxq, which was the Ordnance Code for the Haenel Company. It also may have the pistol serial number stamped on the aluminum base. If so, that's important.
The acceptance marks on the right side of the pistol could be either an eagle-over-655, or an eagle-over-135, or one of each. This too is important in the evaluation.
The grips, if authentic, are bakelite material and some refer to the Luger as a "Black Widow", but that is not an official name.
The rest of the information is a grading of the finish and condition of the bore. It is difficult to tell from the photos.
Well at least it's a start. <img src="graemlins/beerchug.gif" border="0" alt="[cheers]" />