Chaucer, Geoffrey. A Treatise on the Astrolabe, addressed to his son, Lowys, A.D. 1391, edited by Walter Skeat, London (1872). The first book on the subject written in English. Not very useful, but a good place to start and widely available. Search Google Books: http://books.google.com
Grant, Edward. A Sourcebook in Medieval Science, Harvard University Press (1974) Not much in here about the astrolabe, it is only mentioned a few times in passing. But there is a very nice geometric proof for the function of the shadow squares, and John of Sacrobosco’s “On the Sphere” is a wonderful discussion of the Ptolemaic Earth-centered theory that underlies the design of the astrolabe. http://amzn.com/0674823605
King, David A. A Survey of Medieval Islamic Shadow Schemes for Simple Time-Reckoning. Oriens, Vol. 32 (1990), pp. 191-249 Gives the background theory for the shadow squares and their relationship to timekeeping. Can be found on JSTOR, if you have access.
Morrison, James. The Astrolabe, Janus, 2007 This is the definitive work on the history, design, construction and use of the astrolabe, and a host of related instruments. Required reading for anyone interested in the Astrolabe. If you can buy just one book, it should be this one. http://amzn.com/0939320304
Neugebauer, O. The Early History of the Astrolabe. Studies in Ancient Astronomy IX, Isis, Vol. 40, No. 3 (Aug., 1949), pp. 240-256. Historical background on the astrolabe. Can be found on JSTOR, if you have access.
Pingree, David and Chandler, Bruce. Eastern Astrolabes (Historic Scientific Instruments of the Adler Planetarium Series; Volume II), Adler Planetarium, 2009 A catalog of astrolabes and related tools in the Adler Planetarium collection. Very good, detailed photos of actual working astrolabes. An excellent reference. Volume 2 focuses on Middle Eastern and Near Eastern devices.
Stoeffler, Johannes. Elucidatio fabriquae ususque astrolabii, Oppenheim (1523). The original of the book translated below. A scanned pdf of the original Latin text is available online at: http://www.univie.ac.at/hwastro/books/1513_stoe_ColMed.pdf
Stoeffler, Johannes. Stoeffler’s Elucidatio – The Construction and Use of the Astrolabe, English translation by Alessandro Gunella and John Lamprey, Classical Science Press, 2007 This is a translation of a 16th century manual on the construction and use of the astrolabe; expensive, but second only to Morrison’s book for usefulness. http://www.classicalsciencepress.com/books/Stoefflers-Elucidatio-John-Lamprey.html
Webster, Roderick. Western Astrolabes (Historic Scientific Instruments of the Adler Planetarium Series; Volume I), Adler Planetarium, 2007
A catalog of astrolabes and related tools in the Adler Planetarium collection. Very good, detailed photos of actual working astrolabes. An excellent reference. Volume 1 focuses on European devices.