The Battle of Agincourt is rather well documented for an event of the 15th century. Perhaps the most famous source in English-speaking countries is Shakespeare's play Henry V. Many military historians have contributed articles and books on this topic. Books that are in print can be purchased as local shops or online bookstores such as Amazon.com.
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The Face of Battle by John Keegan, 1976, Chapter 2
Keegan, probably the best-known military historian at present, chose three battles with which to illustrate how men function in warfare. Agincourt is the first of the three. A reasonably-priced softcover edition by Penguin Books is widely available.
Agincourt 1415: Triumph Against the Odds by Matthew Bennett, 1991
This 96-page paperback volume is an excellent all-around reference about the battle. Sections describing the commanders, armies, and campaign precede discussion of the battle itself. The pages are lavishly illustrated with photographs, maps, diagrams, and color plates of some of the participants. A short section at the end of the book gives information about the battlefield as it stands today.
The Armies of Agincourt by Christopher Rothero, 1981
This short (40 pages) paperback is notable for its eight color plates of participants in the battle. The extensive notes about each individual pictured are printed in French and German on the final page. Text sections cover the campaign and battle.
Great Commanders and Their Battles by Anthony Livesey, 1993, pp. 36-43
Generals from Alexander the Great to Robert E. Lee to Douglas MacArthur are profiled in this "coffee table" book. The pages on Henry V and Agincourt summarize the campaign and battle compactly. The two-page painting of the battlefield is well-done.
A reading of William Shakespeare's play The Life of Henry the Fifth provides some background for the campaign that resulted in Agincourt. The play is available as a separate title or in collections such as The Riverside Shakespeare. The text of Henry V is available on the Web.
A guide to the play will provide information about the battle in addition to explaining the text. For example, Asimov's Guide to Shakespeare devotes two pages to an analysis of the result of the fighting.
Crispin's Day: the Glory of Agincourt by Rosemary Hawley Jarman, 1979
Agincourt by Christopher Hibbert, 1978
Agincourt, October 25, 1415 by Mary Cathcart Borer, 1970
Agincourt by Charles Kightly, 1974
Shakespeare's Agincourt by D. K. C. Todd, 1985
The Agincourt War by Alfred H. Burne, 1976
History of the Battle of Agincourt by Nicholas Harris Nicolas, 1970
The Battle of Agincourt: a Collection of Contemporary Documents by Howard Loxton, 1966
Famous Land Battles, from Agincourt to the Six-Day War by Richard Humble, 1979