Abstract: Space is a concept that is fundamental to all branches of physics; it is also central to neuroscience. We think not only about physical space but also about abstract spaces that allow us to geometrize complex problems. Inside your head, your brain represents space as a pattern of neural firing, produced and maintained by neural circuits in the hippocampal formation. In this talk, I will explain the organization of these circuits and systems that build the brain's internal description of space. I will then discuss how these systems self-organize to produce a cognitive map: a way of imagining location in physical and abstract spaces.