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Bernard Cornwell (OBE) is a British writer living and working in the United States. I believe he is one of the biggest-selling living writers of historical fiction in the world today, and almost certainly the biggest-selling living British historical writer. His books tend more towards drama and action-adventure than historical fidelity, but still do a reasonable job of bringing alive historical periods the reader may know little about. He was heavily influenced in his writing (like GRRM) by George MacDonald Fraser's Flashman Papers series, but Cornwell doesn't have as strong a sense of humour. Thus his heroes tend to be much more straight-laced and traditionally heroic.
The Sharpe Series (1981, ongoing, books listed in chronological order)
Sharpe's Tiger, Sharpe's Triumph, Sharpe's Fortress, Sharpe's Trafalgar, Sharpe's Prey, Sharpe's Rifles, Sharpe's Havoc, Sharpe's Eagle, Sharpe's Gold, Sharpe's Escape, Sharp's Fury, Sharpe's Company, Sharpe's Sword, Sharpe's Skirmish, Sharpe's Enemy, Sharpe's Honour, Sharpe's Regiment, Sharpe's Christmas, Sharpe's Siege, Sharpe's Revenge, Sharpe's Waterloo, Sharpe's Devil.
The adventures of Richard Sharpe who rises from a footsoldier in Sir Arthur Wellesley (aka the Duke of Wellington)'s Indian army helping in the conquest of India in the 1790s to become a senior figure in Wellington's army during the Peninsular War (1808-1814) and the Waterloo campaign. The final book sees Sharpe getting embroiled in the Spanish colonial war of independence in South America in 1820, and brings Sharpe face-to-face with Napoleon when they stop off at his island prison along the way.
Sharpe was turned into an irregular ITV TV series which made an international star out of Sean Bean (who later found even more fame as Boromir in the Lord of the Rings movies).
The Starbuck Chronicles (1993-96)
Rebel, Copperhead, Battle Flag, The Bloody Ground
This series is set during the American Civil War.
The Warlord Chronicles (1995-97)
The Winter King, Enemy of God, Excalibur
A historical take on post-Roman Britain and King Arthur which downplays the mystical elements.
The Grail Quest (2000-2003)
Harlequin, Vagabond, Heretic
A quest for the Holy Grail set during the Hundred Years' War.
The Saxon Series (2004, ongoing)
The Last Kingdom, The Pale Horseman, The Lords of the North
A possibly open-ended series (like Sharpe) set in 9th Century England and focusing on King Alfred the Great.
George MacDonald Fraser is an experienced journalist and writer. He also served in the British Army in India. He is now in his eighties. He is the author of several well-received standalone novels (such as Black Ajax and The Pyrates) and several films, including the James Bond movie Octopussy, but is best known for the excellent Flashman Papers series of novels. The central conceit of these books is that they are the memoirs of an incorrigible rogue and rake who got by in the British Army with a great deal of luck and horrendous bad luck landing him in the most dangerous places on Earth, but somehow coming out with medals. He is quite clearly part of the inspiration for Tyrion in ASoIaF, though with only a tiny shred of honour to his name.
The Flashman Papers (1965, ongoing, books listed in chronological order)
Flashman, Royal Flash, Flashman's Lady, Flashman and the Mountain of Light, Flash for Freedom!, Flashman and the Redskins, Flashman at the Charge, Flashman in the Great Game, Flashman and the Angel of the Lord, Flashman and the Dragon, Flashman on the March, Flashman and the Tiger
Flashman is notably superior to Cornwell's books mainly because Fraser invents very little in them. Virtually every character and incident is either real, or borrowed from a Victorian novel of the time (Flashman himself first appeared as a school bully in the Victorian novel Tom Brown's School Days). The only major suspension of disbelief is that Flashman could survive through all of his adventures to die at the ripe old age of 92 (when the brothel he is in is accidentally shelled by the Germans during WWI) and the sheer number of different military adventures he gets involved in, from the Afghan Rising of 1839-42, to the Crimean War (where Flashman accidentally ends up leading the Charge of the Light Brigade), the Sikh War and Indian Mutiny, the Taiching Rebellion in China, Harper's Ferry and the American Civil War (where Flashman ends up serving both sides and plays an as-yet undisclosed role at the Battle of Gettysburg), the Borneo Pirate Wars, the Boxer Rebellion in China, the last of the American Indian Wars (where Flashman is the sole survivor of Little Big Horn), the Australian Gold Rush, the War of 1870 between France and Prussia, the Zulu War (where Flashman is one of the defenders of Rourke's Drift), the Boer War and much, much more.
Frankly, the books are brilliant and well worth reading. The collective effect of the books is to demonstrate to the reader exactly how the hell Britain ended up controlling one-quarter of the globe and managed to hold on to it for nearly a century and a half. Great stuff. The only major problem is that Fraser is getting on now and has yet to write the biggest missing piece of Flashman's life, namely the American Civil War. This is more annoying because the novel Flashman and the Dragon ends on a cliffhanger that leads into the civil war storyline, but we then move on eight years to Flashman fighting in Ethiopia in Flashman on the Charge. Slightly irritating.