Here are the most valuable books I have found on Atlantis, the lost city, continent, empire. Most links are for more info at Amazon.com, an affiliate.
The Atlantis Dialogue: Plato’s Original Story of the Lost City, Continent, Empire, Civilization, by Plato, translated by B.Jowett, edited by Aaron Shepard, Shepard Publications, Los Angeles, 2001. A contribution of my own, presenting everything Plato said about Atlantis, in the context he intended. If you have never read Plato in the original, this could throw new light on the subject.
Lost Continents: The Atlantis Theme in History, Science, and Literature, by L.Sprague de Camp, Dover, New York, 1970. A detailed survey of the Atlantis idea, its history, and arguments for and against the continent’s existence. The most enlightening book I’ve ever read on the subject!
Atlantis: The Antediluvian World, by Ignatius Donnelly, Dover, New York, 1976. A reprint of the 1882 book that most popularized the Atlantis myth and that provided arguments still repeated today. The introduction by E.F.Bleiler provides critical, historical perspective.
Mysteries of Atlantis Revisited, by Edgar Evans Cayce, Gayle Cayce Schwartzer, and DouglasG. Richards, St. Martin’s, New York, 1997. Though avowedly from the camp of the American psychic Edgar Cayce, this is a relatively balanced and objective look at the topic, including recent explorations.
Atlantis: Insights From a Lost Civilization, by Shirley Andrews, Llewellyn, St. Paul, Minnesota, 1998. A good book for seeing how a variety of people have described Atlantis. Unfortunately, all the author’s sources are jumbled together without discretion—but her detailed notes in back can help you separate the strains.