The historian Adrian Goldsworthy has made quite a successful career out of writing (normally very good) books about Rome and her military- depending on which era, I'm sure you can find something in his published works that could suit. Personally I'm very fond of In The Name of Rome: The Men Who Won The Roman Empire, which examines the changing nature of Roman warmaking using specific personalities (starting with Fabius Maximus and Claudius Marcellus in the Second Punic War, he works his way through to Belisarius and the Battle of Dara).

You should take a look at Carl von Clausewitz's Vom Kriege (On War) and Antoine-Henri Jomini's The Art of War. Both are early 19th century texts, but both were also popular teaching tools and had a lasting impact (it is probably safe to assume, for example, that every member of the German High Command in the First World War had read Clausewitz). Hew Strachan has also written a slim volume examining the history and impact of On War, called Clausewitz's On War: A Biography

For the early period, I would start with the classics - Thucydides, Herodotus, Tacitus, Caesar's Commentarii de Bello Gallico (Commentaries on the Gallic War). The Romans are not my specialty, however, so I apologize for not being able to suggest more.

I would recommend having a look at Peter Paret (ed). Makers of Modern Strategy: Military Thought from Machiavelli to the Nuclear Age (Princeton: Princeton University Press, 1986) and Russell F. Weigley's The American Way of Warfare: A History of United States Military Strategy and Policy (New York: Macmillan, 1973). The first is a collection of essays that explores military thoughts across time and space. The second focuses on American military thought from the Revolution to the 1960s.

For tactics, in particular the use of artillery, see Shelford Bidwell and Dominick Graham's Fire-Power: British Army Weapons and Theories of War, 1904-1945 (London: Allen and Unwin, 1982) and John A. English and Bruce I. Gudmundsson. On Artillery. (Westport, CT: Praeger, 1993).

For military thought and philosophy, as u/lureynol points out, Clausewitz and Jomini are important figures. However, instead of reading what can be fairly antiquated prose, I suggest reading Hugh Smith's On Clausewitz: a Study on Military and Political Ideas (New York: Palgrave Macmillan, 2005), which offers a great introduction and analysis of the context in which Clausewitz lived/wrote. You might also be interested in Elisabeth Krimmer and Patricia Anne Simpson, Enlightened War: German Theories and Cultures of War from Frederick the Great to Clauswitz (Rochester, NY: Camden House, 2011).

Some of these are dated, but are classic "war and society" texts. If you need any further suggestions, do not hesitate to ask. I hope this helps.

I can't go into much detail because I'm on my phone, but you may want to check out The Sling and The Stone: On War in the 21st Century by Thomas X. Hammes. In it, he divides warfare into four distinct 'generations'. The first involved old-fashioned line battles, and lasted up to around the late nineteenth century.

The second generation lasted through World War I and was characterized by the use of new weapons such as improved artillery, poison gas, and machine guns, along with nations ability to mobilize mass numbers of young men and arm them through the industrialization of warfare.

The third generation began with the Second World War, and saw the introduction of large-scale maneuver warfare involving armored vehicles and increasingly mobile infantry forces. This style of warfare remained dominant through most of the twentieth century, and it's the style for which most modern military forces are trained and equipped.

The fourth generation can be described as a type of war where victory is achieved by slowly eroding the enemy's political will to fight, popularly referred to as an 'insurgency'. We've seen this type of warfare since at least the middle of the twentieth century--it's the type that the Chinese Communist Party used to defeat the Kuomintang--but it's become increasingly popular, especially among non-state actors, in more recent decades as it gives smaller, weaker forces the ability to defeat large, well-trained, and well-funded armies.

The Sling and the Stone is mostly about fourth generation warfare, but in the book, Hammes makes an interesting observation about all four: With each successive generation of warfare, the primary objective of the military forces has moved further back from the front line. In the first generation, each army sought simply to defeat the other side's forces. In the second, the primary target of newly-developed artillery weapons became the enemy's support and communication units. In the third, forces attempted to maneuver even deeper behind enemy lines, later even attacking strategic targets in cities in the hopes of destroying the enemy's war industry to secure an easier victory. With the fourth generation, the objective moves back even further, into the hearts and minds of the citizens of the enemy nation.

There's a lecture by Hew Strachan on the "canonization" of strategic thinking that you might be interested in: https://m.youtube.com/watch?v=FHWyffZn5-c

He discusses the development of such a canon over time (from specific thinkers to sort of amorphous strategic doctrines) and its uses, mentioning quite a lot of books and thinkers along the way.

No one yet has mentioned the Byzantine Strategikon as well as the De Re Militari by Vegetius, which ended up having a large impact on warfare of the Middle Ages.

Edit: Does anyone have recommendations on books on military logistics?

Stephen Biddle's Military power takes a good look at all the strategic and operational systems that make up modern tacticsz He argues that since 1917 all armies that have succeeded in war share the same emphasis on concealment, cover and maneuver called the Modern System and that Firepower isn't as powerful as assumed by many.

Paddy Griffith also. Forward into battle is a good example of a book focused on small scale unit tactics.