MtGox, called "Mount Gox" or "MTGOX", has been the most widely used bitcoin currency exchange market since it was started, and remains the largest in terms of popularity and volume.
A registrant on MtGox has at least two sub-accounts: one for bitcoins (BTC), and one for US dollars (USD or MTGUSD) or other national currency. Bitcoins are bought using funds from the trader's national currency account, and the proceeds from the sale of bitcoins are deposited into the same account. Trading must always involve bitcoins as trading between different national currencies is not offered.
Trades on Mt. Gox's execute from balances on deposit with the exchange which in turn makes trading on the market instantaneous, compared to some other Bitcoin markets where a subsequent settlement occurs manually between the trading partners. The disadvantage of this is that a third party must be trusted with keeping the money safe.
MtGox was originally started by Jed McCaleb in July 2010, and was sold to Tibanne Co. in Japan in March 2011. It is currently operated by Tibanne Co., managed by Mark Karpeles (MagicalTux).