The introductory chapter provides an excellent overview.
The aura of Alif: the art of writing in Islam
The chapter "Arabic Calligraphy" provides an excellent introduction. Other chapters discuss topics such as calligraphy on coins, architecture, and trucks.
Islamic calligraphy
Most comprehensive book on the topic.
The rise of Islamic calligraphy
Traces the evolution of Islamic calligraphy
The art of the pen: calligraphy of the 14th to 20th centuries
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
Unlike other books, the focus of this work is on the tools and materials of the calligrapher.
The splendor of Islamic calligraphy
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.
