In
Grant Morrison's comic book saga
The Invisibles, the Invisible College is what lies on one side, the positive side, of the overlap between two
parallel universes. The overlap itself is
our universe - think of a
Venn diagram, in which two circles share an
almond-shaped area between them: that's where we live. In Morrison's cosmology, a positive and a negative universe have overlapped and are slowly drifting apart. When they separate in
2012, our reality ends and we are all released into what Morrison calls the
supercontext.
Along the thin line that separates our reality from the greater mass of the positive universe, is the Invisible College. As King Mob says in the issue in which we get the best look at the College (issue 6 of Volume 2, the superlative "The Girl Most Likely To"), "Our reality's the pattern on the wallpaper and this place is the wall." The entity/satellite Barbelith acts as a sort of gatekeeper to the College, although the College certainly isn't the only place people can go when they encounter it.
On approach, the Invisible College looks a bit like the Parliament building gone haywire, or a dream Leonardo da Vinci would have had if he'd been Victorian. It makes sense that the humans in the Invisibles would perceive what they call the Invisible College this way, as the term does have a history in Europe. (At one point in the series, a flashback to a carriage ride with Mary Shelley depicts an unidentified proto-Invisible referring to a secret society called the Invisible College.)
The College seems a lot more structured than its dark-universe counterpart, the Outer Church. It isn't like Morrison to set up order-vs.-chaos dualities like that, or at least, not with order on the side of good. Indeed, most of the verbal ideas going into the Outer Church suggest it as a machine world, whereas its visuals are chaotic.
Actually, different characters' experiences of the College are orderly to different degrees, as we see in "The Girl Most Likely To" when, in their leisurely travels around the crystalline fountains, lofted walkways and open spaces of the wrought-iron-and-spun-sugar space that surrounds them, King Mob and Ragged Robin find themselves at a sort of operating table where several entities (possibly sentient, possibly not, but definitely resembling gray aliens at least facially) materialize from nowhere to treat Robin's wounds. King Mob refers to them as "antibodies." Their presence triggers the long flashback/forward sequence of the issue. In Volume 1 of the series, Liverpudlian street punk Dane experiences a kind of operation/cleansing at the hands of similar entities after his second encounter with Barbelith, and at the beginning of Volume 2, Bruce Wayne analogue Mason Lang describes his childhood experience of alien abduction, which followed a brief encounter with what was almost certainly Barbelith.
The Invisible College can also act as a kind of shortcut between physical locations, as you do in fact leave space when you go there. Whether it's the same as, or connected to, the otherworldly spaces King Mob travels through in the second storyline of Volume 1 and Mister Six uses later in Volume 2 (we only follow him as far as Barbelith that time) is unclear.
Sources: Anarchy For The Masses: An Underground Guide To The Invisibles, Patrick Neighly and Kereth Cowe-Spigai, Mad Yak Press; the original series, DC/Vertigo.