A definitive overview of the events leading up to, and following, the discovery of Neptune in September 1846 - a triumph for the mathematicians who, from its gravitational influences on Uranus, predicted its position so accurately. This second edition will be published to coincide with the 150th anniversary of the discovery of Neptune. This book summarizes how our knowledge of this distant planet steadily grew, and represents material collected from a wide range of sources over many years. The research concerning Neptune, undertaken prior to the Voyager 2 fly-by of the planet in August 1989 is included, as is new material obtained following the encounter of Voyager 2 with Neptune.