This is an older style 1940's-1960's Löwenbräu Muenchen half liter beer krug. This one looks like it may may been made for export as the bottom is stamped "Made in Germany." Decent "as found" condition - it needs a good cleaning before it could be used. The glaze / finish on the inside seems a bit crude. There are some bumps and a bit of extra ceramic dripped in the bottom. There are some dark splotches inside as well. Great item for events to help eliminate farby bottles.
This is a krug, not a stein. Stein is what English speakers and tourists say. In German a stein is a stone. This is a beverage container, not a rock!