Enherited Luger, what do I have?

[NISMOMIKE]

I am new to this forum and was referred here by a user from Calguns forum on Tapatalk. They said this is the top site/forum for the info I am interested in finding. So here goes,
my Mother was just handed down a pistol through unfortunate circumstances. Now that the dust has settled, she and I are interested in finding out about it. What do the markings mean, what would it have been used for? The pistol is numbers matching from what I can see without dissassembly, but magazine is not. I am very unfamiliar with antique firearms. My mom is not anti gun whatsoever, but she does not want the responsibility of having a gun in her house and will likely give it to me. Any info would be great! Thanks everyone.