Brian Williams writes a pretty good book in his Conquerors of Everest. It has an unfortunate title, but generally publishers come up with overly dramatic and generally stupid titles as a stipulation of a book's being published, so I won't hold it against Williams. His content, thank heaven, is not so over-the-top! Williams takes the story of Mount Everest from the initial mapping of the mountain up to the current (1979) climbs, focusing the book on the story of Tenzing and Hillary and their 1953 ascent.
His information is mostly good, with a couple blunders, but considering the amount of info he squeezes into a 30-page book, he does a decent job. Perhaps the one section to pass up is the two-page spread labeled "Chomolungma," in which the surveyors of the 1850's measure the mountains with trigonometry (mostly right), they never got closer than 90 miles to the Himalayas (Everest...), and the locals told them the name of the really tall peak, Chomolungma, and its satellite peaks Changtse, Lhotse, and Nupste, (named by George Mallory), but the surveyors still wrote it down as Peak XV (jerks!). A couple small things in addition include a map that shows the early expeditions climbing from the main Rongbuk Glacier up past the North Col to the Northeast Ridge, and also a passage that erroneously says that Doug Scott and Dougal Haston spent the night on the South Summit on their way to the top in 1975.
This book is an OK read if it's immediately available, but there's no reason to seek it out. For a young readers' history of climbing Everest, I'd recommend Audrey Salkeld's Climbing Everest. For a kids' book about the 1953 first ascent of the mountain, I had a lot more fun with Ian Graham's You Wouldn't Want to Climb Mount Everest.