Well the tall cylinder is a graduated cylinder, and the round thing is a round bottom flask. Easy ones out of the way.
The other one appears to be a very highly specialized piece of distillation equipment. It is a quite bizarre one. It was probably built to do one specific reaction. Something this unique is almost a treasure in itself. It looks very difficult to make. Did your Aunt work in a field that might give us a hint?
If someone on this forum can't ID it precisely, give the chemistry subreddit a shot.