From the Earth to the Moon; and, Round the Moon (World Classics, Unabridged) - Jules Verne

Set at the end of the American Civil War, From the Earth to the Moon is a forward-looking tale of space adventure. With no other pressing assignments the Baltimore Gun Club, at the urging of its President, Impey Barbicane, decides to build a gun large enough to propel a projectile from the Earth to the Moon. With a wager being placed on the outcome and the mission being elevated to a 'manned' mission, a space race to the Moon begins.