The Oxford History of Board Games is a very thorough book that discusses board games from their ancient inception to the (almost) present-day dividing into Race Games, Space Games, Chase Games, Displace Games, and War Games (such as chess).
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While not a direct answer, check out the recent " Hobby Games, the 100 best " book.
It has games from the last 100 years and there is a lot of history contained within its page.
Each entry is written by a game designer as well.
I enjoyed the book very much, learned a ton.
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I think A History of Board Games Other Than Chess is one of the definitive books in this category.
The Library Thing page I linked to also has several related books to check out.
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R.C
Bell wrote several books on board games, though I don't think they were as structured as the Oxford book that Jeremiah already mentioned.
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Dork Tower #34: A Brief History of Gaming is a comic book featuring the early history of board games.
John Kovalic is the author/illustrator (he is also a game designer) who created Dork Tower, a comic book that frequently features gaming of all kinds.
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I am currently reading (and very much enjoying) A World of Chess: Its Development and Variations Through Centuries and Civilizations , by Jean-Louis Cazaux and Rick Knowlton.
It's very much specific to chess, but of course chess was and continues to be a big part of the history of board games.
What I'm finding particularly awesome about the book is that it goes into the mechanics of chess in each of its many incarnations over the times and places its been played.
Anyone interested in this topic (history of board games) will absolutely find it fascinating.
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Is there a good book about the history of board games?   Preferably the book would cover all the way from the ancient games to the newest fads in the market.
History of board games
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Try the Oxford History of Board Games, A History of Board Games and a Brief History of Gaming. The  Oxford History of Board Games  is a book that goes into great depth discussing board games from their ancient inception to the present-day. It is divided into Race Games, Space Games, Chase Games, Displace Games, and War Games (including chess).  A History of Board Games Other Than Chess  is another book in this category. Dork Tower #34: A Brief History of Gaming  is a comic book that features on the early history of board games.  
The  Oxford History of Board Games  is a book that goes into great depth discussing board games from their ancient inception to the present-day. It is divided into Race Games, Space Games, Chase Games, Displace Games, and War Games (including chess).   A History of Board Games Other Than Chess  is another book in this category. Dork Tower #34: A Brief History of Gaming  is a comic book that features on the early history of board games.  