I recommend starting with The Cambridge Illustrated Atlas of Warfare: The Middle Ages, 768-1487. While it starts in the mid-8th century, it's written in a way that will help you gain an understanding of medieval strategy and has some good battle diagrams.

Next, I recommend both volumes of David Nicolle's Medieval Warfare Source Book, which is a superb and easily accessible set that traces the evolution of Eurasian warfare from 400-1400 AD (although it's unfortunately somewhat limited with regards to southern India, South East Asia, China, Korea and Japan). It's very helpful with regards to showing Roman influence and how this eventually changed in Byzantium, Europe and the Islamic world. You could actually read just these without the Illustrated Atlas, but I do find Nicolle a little lacking with regards to explaining and illustrating the basics of strategy - he describes the variations and general strategies of different regions well enough, but there's just not the basic theory or enough clear diagrams for a beginner - so I do recommend reading them second.

Unfortunately David Nicolle doesn't trace the evolution of warfare beyond the fourteenth century. To fill the gap, I suggest both volumes of Ian Heath's Armies of the Middle Ages. They cover the European, Islamic and Central Asian world from 1300-1500. Unfortunately they are getting on in age a bit, lack diagrams and only cover organisation, tactics and equipment, although they do have many excellent drawings of soldiers. Flaws aside, they're probably your best bet for going through to the Renaissance.

(As an aside, all of Ian Heath's Wargames Research books are useful supplements to David Nicolle, although they must be used with caution. While Ian Heath is mostly a careful writer, some of his scholarship is outdated and he lacked the specialised language skills - and extra decade and a half of research - David Nicolle has. For the most part, Ian Heath is a good addition to Nicolle, but wherever there's conflict, trust Nicolle over Heath and always be wary of taking Heath's larger numbers at face value)

If you want to delve deeper on the European side of things, I recommend Guy Halsall's Warfare and Society in the Barbarian West 450-900 and John France's Western Warfare in the Age of the Crusades 1000-1300. Unfortunately, I haven't been able to find a good synthesis on warfare in the Late Middle Ages, but some useful information is contained in Philippe Contamine's War in the Middle Ages, specifically Chapters 4, 5 (pages 188-192 only, ignore everything else in the chapter) and then chapters 6-10.