Here is a list of what are probably the most often cited books on internal ballistics. Most of them are freely available online in a pdf version.
C. S. Robinson “The Thermodynamics of Firearms” McGraw Hill, 1943
This has the virtue of being the first book on internal ballistics printed in English. Up to this point, all of the open literature on internal ballistics was published in French, German or Russian. Research in English and American ballistics laboratories had been published as internal reports, not available to the public. The book goes into detail on the thermochemistry of burning powders, but has very little to say on the modelling of the internal ballistics of guns. Not available online that I can find.
J. Corner “The Theory of the Interior Ballistics of Guns” Wiley, 1950
This is the “classic” text on the theory of “classical” internal ballistics. Every serious student of internal ballistics should have this on their bookshelf. It is basically a statement of the state of the art in British research at the end of WWII, when the British had hugely stepped up their experimental and theoretical research efforts in internal ballistics, funded by the large budgets that suddenly became available for their work. This is available online.
F. R. W. Hunt “Internal Ballistics” The Philosophical Library, 1951
This is an edited collection of contributions by a number of British ballisticians. It goes into the basic theory of internal ballistics in some detail and there is a good description of the experimental work and methods that is missing from Corner’s book. This is available online
“Elements of Armaments Engineering - Part Two Ballistics” Engineering Design Handbook, AMCP 706-107, 1963
This book covers internal and external ballistics and does a good job of the basics. It does not go into any serious detail though. This is available online
“Interior Ballistics of Guns” Engineering Design Handbook Gun Series, AMCP 706-150, 1965
This is a more serious effort and is on a par with Hunt’s “Internal Ballistics” in its scope and depth. It is interesting, though, that the experimental methods described date from the war twenty years earlier, and this book is not an advance on Hunt. This is available online
L. E. Brownell “Elements of Internal Ballistics - Russo-German Methods” Appendix III, University of
Michigan Technical Reports in Internal Ballistics” 1966
This is mainly a translation of chapters 1 through 5 of a German text, “Innere Ballitick”, by Waldemor Wolff, 1961. This was written in some frustration by Brownell, who could not find any printed works in English. Brownell wrote, “When Michigan investigators looked for unclassified U.S. literature on ballistics they found it to be almost non-existent. The reasons for this seem to be that 1) the United States Army classifies nearly all of its ballistic research; and that 2) there is no journal in the United States which is suitable for printing technical articles on ballistic research. Therefore, the Appendices are an attempt to alleviate this problem in part by presenting technical articles from the University of Michigan”
This work is notable in that - as far as I can see - it is the first description in English of how vivacity is related to the burning rates of powders. This is now commonly used by powder companies to quantify the burning rate of their powders.
Not available online that I can find, except in a simple text version, which makes the equations unintelligible.
SERABRYAKOV, M. E. “Interior Ballistics”, 1949. Available in English from Air Technical Intelligence Translation, Wright-Patterson Air Force Base, Ohio, 1968
This was the text book for Soviet schools of military science and shows how ballistics evolved in a parallel but isolated way from ballistics in the West. It does not actually add very much to the body of knowledge than can be found in the main English texts of this period though. This is available online
H. Krier, M. Summerfield “Interior Ballistics of Guns” Progress in Astronautics and Aeronautics, Vol. 66, 1979
This book contains much of the material of the earlier 1965 work of the same name. But it brings the state of the art up to date and describes how the main topic of research was now the potentially destructive pressure waves that could occur in guns, and how to mitigate this by suitable ignition methods. Not available online that I can find.
“Handbook on Weaponry” Rheinmetall, 1982 (Translation of "Taschenbuch fur den Artilleristen” )
Rheinmetall in Germany had published a handbook since the 1930’s but it was in German and after repeated requests, they produced an English version in 1982. It covers the basics and is thorough in a Germanic sort of way. This is available online
C. L. Farrar, D. W. Leeming “Military Ballistics - A Basic Manual” Brassey’s Defense Publishers, 1983
This book was written for officers attending the Royal College of Military Science at Shrivenham in England. It is somewhat abbreviated, but all the basics are there. It has a surprisingly good section on closed bombs. Not available online.
D. E. Carlucci, S. S. Jacobson “Ballistics - Theory and Design of Guns and Ammunition” CRS Press, 2013
This is a text book covering internal ballistics, transitional ballistics, external ballistics and terminal ballistics. It scampers through internal ballistics in just 100 pages and suffers in intelligibility as a result. It is also rather unbalanced, spending ten pages deriving the Lagrange pressure gradient equations which should only have taken two pages. Sidney Jacobson’s contribution to the “Interior Ballistics of Guns” in 1979 was far more thorough and readable. Surprisingly, this is available online - and in a version which has more detail in it than the book.