Generally thought of as O'Brien's masterwork, though personally I prefer the more structured lunacy of The Third Policeman. It must be the third time at least that I've read it, but only the first time that I've tried to write down what I think it's about.
There is a lot more sex in it than I remembered, but women are barely visible except as seen by men - there's only one speaking human female character (plus a cow plus perhaps the Good Fairy). Oddly enough the cover of this edition is a picture of a man and a woman by Jack B. Yeats, with the two separated by the spine of the book so that they are apart rather than together as the artist intended.
One can imagine the origins of the book as being a series of fantasies told in the pub, especially the all-male Dublin pub environment of the 1930s. It's about telling stories and the tellers of stories; it's about confronting the epic with the demotic; it's about the supernatural encountering the familiar; it's about a student, a hotel full of characters and Sweeny the wanderer. It's quite hard work to read as well.
I still like The Third Policeman more, but I can see why people get obsessed with At Swim-Two-Birds.