As the others have said, yes, they're mammals (what else could they be??). In German, they're called "Fliedermaus" - the mouse with wings, which is quite a good description, although bats (in Britain, at least) eat insects and are great at controlling mossies and moths. They are totally harmless to us and anyone who has bats around should be honoured! I have pipistrelle bats nesting on my land and they're lovely to watch. My little cat, Cleo, climbs up on the dairy roof in the summer, to try and catch them, but hasn't succeeded yet, thankfully!! (They're too fast for her!)