Watch the The Edge online guitar lesson by Jeff McErlain from Kings of Tone
The Edge's guitar collection is quite extensive as you can imagine. If you don't believe me I recently read an article listing his touring guitars, there are 43 in total! But according to him the first guitar that defined his sound was his Gibson Explorer. He also uses a 70's Strat that was seen in many of the band's videos in the 1980's. For me his sound is less guitar specific as it is amp specific, namely the Vox AC30.