Often referred to as "Asia House". Quadrangle is a U-shaped building surrounding a courtyard; what would be the open end is cut off by Bosworth Hall, and Fairchild Chapel projects into the middle of the courtyard.
Historically, the Quadrangle was the house of the Graduate School of Theology from the 1920's to the 1960's, when the school was sold to Vanderbilt.
"On the outside, the Quad is one of the most beautiful dorms on campus, with a wonderful courtyard. On the inside, the hallways are surprisingly dark, though they are wide. The community, which is focused around Asian and Asian-Pacific-American culture and issues, tends to be welcoming and strong, and the residents are of various races (not just Asian.) It’s a good place to live if you’re an East Asian Studies major or just interested in living in a nice place with a cultural bent. If your only interest in Asia is in Japanese Anime, however, you might want to think again. Asia House also has a hall with apartments--suites with two rooms, a bathroom and a kitchen, usually for two people to live in. They're a really suite..er, sweet deal, if you can get one, as they're the only apartments in campus dorms (aside from, of couse, the Firelands complex). However, the apartment hall has no community at all, and isn't really intergrated into the rest of Asia House either." --ilunas 
"It is absolutely beautiful from the outside, especially in the spring, and is located convieniently near most of the academic/ executive buildings. The hallways are rather dimly lit, however, and the room windows do not offer very good ventilation. Also one of the wings smell funny. Be sure to check out Hell Court--the concrete basketball court thirty feet underground, in the basement." --kittykenko 
"I was misinformed early in the year when someone told me that something was in Asia House (I forget what, but that's not the point). I ended up spending a good half hour wandering around to my great amusement. Asia House has a lot of community: it's very obvious as you walk around and see the notes on everyone's doors and the pictures of the RAs (drawn by the hall people) all over the walls. The dorm itself is gorgeous, one of the (if not the most) prettiest dorms on campus. The rooms are not bad, though I have some issues with the restrooms. The basement is awesome... there's all kinds of random drawings and (as aforementioned) basketball courts [which I assume is just used to smoke up...?]. Awesome place. The co-op inside Asia House is amazingly tasty, though if you don't show up a little early it's easy to not get any food (it's good, they run out)." --rchicken 
"I think the lit says: Gorgeous, nice sized rooms, pretty court yard. Don't know a whole lot about teh community. Houses a good Co-op." --anonymous