I noticed that the Cultus Deorum forum has a great and detailed reading list. I think we need such a list for the Roman military.
These are the books in my personal library on this topic and which I recommend ---
Fields, Nic, and Duncan Anderson. The Roman Army of the Punic Wars, 264-146 B.C. Oxford: Osprey, 2007.
Erdkamp, Paul. A Companion to the Roman Army. Malden, MA: Blackwell, 2007.
Ross, Stewart, and Alan Langford. A Roman Centurion. Vero Beach, FL: Rourke Enterprises, 1987.
Sekunda, Nick, and Simon Northwood. Early Roman Armies. London: Osprey Pub., 1995.
D'Amato, Raffaele, and Giusepppe Rava. Imperial Roman Warships 27 BC -193 AD. Oxford, UK: Osprey, 2016.
Campbell, Brian. The Roman Army, 31 BC - AD 337: A Source Book. London: Routledge, 1994.
Campbell, J. B. War and Society in Imperial Rome: 31 BC-AD 284. London: Routledge, 2002.
Fields, Nic, and SeaÌn OÌ BroÌgaÌin. Early Roman Warrior, 753-321 BC. Oxford: Osprey Pub., 2011.
Campbell, J. B. Greek and Roman Military Writers: Selected Readings. London and New York: Routledge, 2004.
McNab, Chris. The Roman Army: The Greatest War Machine of the Ancient World. Oxford: Osprey Pub., 2010.
Peterson, Daniel. The Roman Legions Recreated in Colour Photographs. London: Windrow & Greene, 1992.
Elliott, Paul. The Last Legionary: Life as a Roman Soldier, AD 400. Staplehurst: Spellmount, 2011.
Renatus, Flavius Vegetius. Roman Military Institutions. Philadelphia, PA: Pavilion, 2004.
Sumner, Graham. Roman Military Dress. Stroud: History, 2009.
McCall, Jeremiah B. The Cavalry of the Roman Republic: Cavalry Combat and Elite Reputations in the Middle and Late Republic. London: Routledge, 2002.
Bishop, M. C., and J. C. Coulston. Roman Military Equipment: From the Punic Wars to the Fall of Rome. London: Batsford, 1993.
Fields, Nic, and Duncan Anderson. The Roman Army: The Civil Wars, 88-31 BC. Oxford: Osprey, 2008.
Fields, Nic, G. A. Embleton, S. Embleton, and Martin Windrow. Roman Battle Tactics, 390-110 BC. Oxford: Osprey, 2010.
D'Amato, Raffaele, and Giuseppe Rava. Roman Centurions: 31 BC - AD 500: The Classical and Late Empire. Oxford: Osprey, 2012.
Simkins, Michael. The Roman Army from Hadrian to Constantine. London: Osprey, 1979.
Cowan, Ross, and Angus McBride. Roman Legionary: 58 BC - AD 69. Oxford: Osprey, 2003.
Phang, Sara Elise. Roman Military Service: Ideologies of Discipline in the Late Republic and Early Principate. Cambridge: Cambridge UP, 2008.
Campbell, Duncan B., and Adam Hook. Siege Warfare in the Roman World: 146 BC-AD 378. Oxford: Osprey, 2005.
Dando-Collins, Stephen. Legions of Rome: The Definitive History of Every Imperial Roman Legion. New York: Thomas Dunne, 2010.
Harris, William V. War and Imperialism in Republican Rome, 327-70 B.C. Oxford: Clarendon, 1979.
Roth, Jonathan P. The Logistics of the Roman Army at War (264 B.C.-A.D. 235). Leiden: Brill, 1999.
Southern, Pat. The Roman Army: A Social and Institutional History. Santa Barbara, CA: ABC-CLIO, 2006.