The Trompowsky Attack (ECO A45) begins 1.d4 Nf6 2.Bg5. White avoids the immense amount of heavily analyzed theory associated with the various Indian Defenses (Nimzo-Indian, Bogo-Indian, Queens-Indian, Dzindzi-Indian, King's Indian Defenses) and intends to chop on f6 inflicting double pawns on Black's pawn structure. It is not a deadly threat, Black can allow it or avoid it if he prefers.
It is named after Brazillian Champion Octavio Trompowsky, who played it consistently during the 1920s and 30s. It is known by two other names as well: Ruth-Opovcensky Attack and "The Zot".
It is still played from time to time at the top levels of chess. Two grandmasters who have played it very often are Julian Hodgsen and Antoaneta Stefanova. Nigel Short employed it against Vassily Ivanchuck in the Capablanca Memorial in 2010. Other top professionals who used it recently in standard time control FIDE rated games (2010-11) include: Lazaro Bruzon Batista, Dmitry Andreikin, Hikaru Nakamura, Teimour Radjabov, Alexander Morozevich and Nikita Vitiugov. Given that the Trompowsky is still seen within top-flight professional chess, as well as considering the super-gms who have used it, it can be fairly characterized as a surprise weapon well suited to those with an imaginative, creative approach to the game. It may even be a bit underrated.
Published books about the opening include:
Gallagher, Joe. (1998). The Tromposky. Chess Press
Wells, Peter. (2004). Winning With The Trompowsky. Sterling
Davies, Nigel. (2005). The Trompowsky. Everyman Chess.
Palliser, RIchard. (2009). Starting Out: The Trompowsky Attack. Everyman Chess.
Below are a few well known and interesting representative games.