This essay is mainly a review of Flat Earth: The History of an Infamous Idea by Christine Garwood (Macmillan 2007). The nine long chapters of this book give a straight-forward chronological account of the history of Flat Earth ideas and their proponents.
However the Prologue "The Columbus Blunder" is more about the "popular misconception" that, apart from a few ancient Greeks, everyone before 1492 thought the earth was flat. Citing Jeffrey Burton Russell Inventing the Flat Earth: Columbus and Modern Historians (1991), the author traces the popularisation of this view to Washington Irving The Life and Voyages of Christopher Columbus (1828), although the story can be traced back further to 1709.
I question her sweeping assertion that: "... the origin and appeal of the Columbus story lie in another mythical world view: the idea that Europe suffered a 'Dark Age' for a thousand years from c.450 to 1450". That this period saw a decline in intellectual endeavour is difficult to dispute, and is not merely an invention of subsequent humanist and enlightenment historians such as Petrarch, Condorcet and Voltaire, as she seems to maintain.
It should also be borne in mind that the Greek view of the Earth, as expounded by Aristotle, was as a stationary globe at the centre of the universe, and with the populated countries at the 'top', the Northern Hemisphere. While Augustine of Hippo (354 - 430) accepted a spherical Earth he was convinced, for scriptural reasons, that people could not live on the other side of the globe. In my view, such an Earth is very little different from a flat one. Two other early christian writers who were definitely flat-earthers were Firmianus Lactantius (c.245-325) and Cosmas Indicopleustes (c.548), but the author maintains that their works, being in Greek and not widely copied, "had no impact in the Latin-speaking West".
The issue of whether the Earth rotated daily, which would mean that the stars were stationary, was considered from physical, philosophical and theological points of view by several late mediaeval thinkers. Thomas Aquinas (1225 - 1274) thought not, because the atmosphere would be disrupted. Jean Buridan (c.1300 - c.1358) and Nicole Oresme(c.1320 - 1382) thought it possible, and came close to the modern view of inertia, but out of caution (or fear of being accused of heresy perhaps) decided for the status quo. Copernicus in 1543 was the true 'revolutionary' in not only setting Earth in motion round the Sun, but rotating it daily on its axis. These issues are ignored in the book.
Chapter 1 is a brief suvey. Chapters 2-4 cover the late Victorian period featuring Samuel Birley Rowbotham (1816 - 1883), known as 'Parallax', John Hampden (1820 - 1891), William Carpenter (1830 - 1896), and others, and in particular the notorious 'wager' with Alfred Russel Wallace in surveying the Bedford Levels, which led to litigation over the years.
Chapter 5 deals with Lady Elizabeth Blount (1850 - 1935) and the Universal Zetetic Society, founded 1893. Chapter 6 with Wilbur Glenn Voliva (1870 - 1942) and the Christian Catholic Apostolic Church in Zion (Illinois).
Chapters 7 - 9 cover the flat-earthers of the space-age period. Chapter 7 is on Samuel Shenton (1903 - 1971) and the International Flat Earth Research Society, founded 1956. Chapter 8 with the more tongue-in-cheek Flat Earth Society of Canada, under Leo Ferrari. Chapter 9 concludes with Charles Kenneth Johnson (1924 - 2001) and the IFERS of America.
Here is a review of the book by 'Flat Earth Believer': The Flat Earth Society Forum. and a history of the Round Earth idea according to Wikipedians.