The History of the Decline and Fall of the Roman Empire by Edward Gibbon is an influential enlightenment account of Roman history from the peak of prosperity under the Antonine Emperors in the second century CE. Originally published in six volumes between 1776 and 1789, the later books bring the story all the way up to the fall of Constantinople in the fifteenth century, taking in the rise of Islam and the Crusades on the way.
Although his methods were soon overtaken by new standards of historical criticism emanating from Germany, Gibbon's preference for primary sources was notable by the standards of his own day. Then and later, most controversy attached to his assessment of the role of Christianity in Rome's decdine. More recently, scholarship of the period now known as Late Antiquity has defined itself against the image of the Dark Ages which Gibbon helped to popularise.
Free online texts
Gutenberg: The History of the Decline and Fall of the Roman Empire, edited by H.H. Milman.
Internet Archive: The History of the Decline and Fall of the Roman Empire. Vol I | Vol II, edited by J. B. Bury (1914). EPUB, MOBI, PDF and TXT formats.
University of Adelaide (Internet Archive): The History of the Decline and Fall of the Roman Empire, with Notes by the Rev. H.H. Milman. EPUB, HTML and MOBI formats.
Wikisource: The History of the Decline and Fall of the Roman Empire. Multiple editions, though each currently incomplete. HTML and other formats.