Before George Mallory died on the North East Ridge of Everest in 1924, he was on Everest twice before. This is the story of the 1921 "Reconnaissance" when the British scouted out the approaches and topography for the first time, and their first official attempt at the summit in 1922. Mallory was on all three expeditions. This is a good recap, with enough detail, but if you want a thorough account, be sure to read Wade Davis's "Into The Silence" (which includes the 1924 expedition.)
Most people agree that Mallory never made the summit in 1924, although there is no evidence to prove he did or didn't, and if he didn't he got reeeeaally close. Conrad Anker found his body in 1999, just below the summit ridge, but Sandy Irvine's body is still somewhere on the mountain, along with the camera they took. I think it is very possible they made it, after studying all the various opinions, which of course would upend the Himalaya saga as we know it, and Edmund Hillary/Tenzing Norgay's 1953 success. Either way, with the South East ridge route eclipsing the popular imagination, thanks in great part to Krakauer's portrayal of the route as over-commercialized, and overwhelmed with client queues, the North East ridge and the West Ridge both hold their mountaineering mystique.