The introductory chapter provides an excellent overview.
The aura of Alif: the art of writing in Islam
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The chapter "Arabic Calligraphy" provides an excellent introduction. Other chapters discuss topics such as calligraphy on coins, architecture, and trucks.
Islamic calligraphy
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Most comprehensive book on the topic.
The rise of Islamic calligraphy
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Traces the evolution of Islamic calligraphy
The art of the pen: calligraphy of the 14th to 20th centuries
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Notable for its many fine illustrations. Also has short chapter introductions that discuss various aspects of calligraphy.
Traces of the calligrapher: Islamic calligraphy in practice, c. 1600-1900
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Unlike other books, the focus of this work is on the tools and materials of the calligrapher.
The splendor of Islamic calligraphy
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Heavily illustrated. Also shows how calligraphy has been used in architecture and contemporary art. The text, though short gives a good introduction to the topics that it discusses.