Officially Bitcoin trading began in July 2010 with MT.GOX, but this was only the first dedicated exchange. Before this however Bitcoin was exchanged for goods as well as money on a peer-to-peer basis. The two transactions I know of where Bitcoins were exchanged for other currencies or commodities (lol) are shown here.
The first ever transaction was famously sent on 12 Jan 2009 by Satoshi Nakamoto to Hal Finney but these 10 Bitcoins were sent free of charge and therefore NOT exchanged.
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