I agree with /u/TRB1783 that The Age of Battles is a fantastic read. You have to look at how warfare evolve holistically. Cavalry is one of the tools of war, and how it evolved is affected by, and affects how, other aspects of war evolved.

This has been discussed in several recent threads, such as this one, and this one.

I also recommend a few more reading material on the subject:

• Jorgenson, et al., "Fighting Techniques of the Early Modern World," ISBN: 0-312-34819-3, 2005.

• D. Parrott, Strategy and Tactics in the Thirty Years' War, in "The Military Revolution Debate".

• D. Eltis, "The Military Revolution in sixteenth-Century Europe," ISBN 0-76070-765-0, 1995.

• F. Tallett, "War and Society in Early Modern Europe: 1495-1715," ISBN: 0415160731, 2010.

If you want a freewheeling overview of how European warfare changed from 1300-1700, try a chapter by C. J. Rogers, "Tactics and the face of battle," from "European Warfare: 1350-1750," a collection of essays edited by F. Tallett and D. J. B. Trim, ISBN 978-0-511-68047-2, 2010. It's probably the single best paper to read on the subject as it discusses not only the "top level view" of battle, but also very pragmatic yet critical but overlooked aspects of how to actually command troops, how to organize them, etc.

I'll now talk about the early modern era in western and central Europe as close-order tercio style infantry rose to prominence. The tail end of the late Medieval era saw the rise of handgunners, starting with the matchlock arquebus and then transitioning into heavier matchlock musket. But there was not yet the socket bayonet that allowed a musketeer to also provide turn his musket into a pike-like instrument, so infantry units had both pikes and handgunners / shot units organized in squadrons to support each other. This is exactly what the cavalry tried to exploit. Charging straight into a mass of pikes isn't an option so cavalry units had to exploit "gaps" in infantry defense.

Reiters / Cuirassiers / Caracole

In the 1500s-1600s, Reiters / Cuirassiers / Caracole cavalry were useful in as far they could harass arquebus & pike formations, at a time when musket fire rate and accuracy were quite poor. Cavalry could not charge head on into a block of pike, so the role had to be adjusted.

In a pitched battle, Cuirassier units harassed enemy formations to break up their cohesion, and then allow friendly infantry to exploit gaps. What does it mean "gaps"? Squadrons of pikes and shot tended to be deployed as such. So the concentration of shot are on the sides of the pike block. Which makes sense because if two pike blocks are to engage, they want their friendly shot squadrons to pour fire from the flanks. The Reiters would attack, in caracole, at the exposed pike block. If the shot squadrons tried to move forward, they themselves may be exposed to the opposing force. Or, the Reiters would harass the sides of the shot squadrons. So there was a lot of coordination at brigade and squad level. Such was the state of pike & shot coordination in that period, up to around 1700.

They would charge at disrupted units, or assist friendly units from the flanks. Cuirassier armor could withstand arquebus fire even at shorter ranges, and Cuirassiers tended to be better trained and disciplined than arquebusiers. As a result, arquebusiers tended to fire their guns at too long a range neither to be accurate against formations of Cuirassier nor to penetrate their armor. These reiter units had good armor and carried weapons for melée, so they were flexible.

Around 1630, Gottfried Heinrich Graf zu Pappenheim famously tied down an entire Protestant army using a small force of elite Reiters in the Westphalian theater of the Thirty Years' War, using his mobility to strike at unexpected weak points.

But over time, as musket improved in accuracy and fire rate (especially thanks to the switch from matchlock to flintlock), and as infantry formations tended to be linear and with less emphasis on pikes, the role of heavy cavalry shifted and the Reiter became unpopular.

Harquebusiers and Dragoons

These were largely developed in France as mounted handgunners that used horses for mobility. German units started to copy them in the 1600s, and the German dragoons fought either dismounted or from horseback. They were otherwise equipped like infantry musket units and were not armored although they carried swords.

Harquebusier cavalry were mounted handgunners carrying the lighter arquebus. They were initially partially armored, but the level of protection declined over time. They often also carried pistols and were reported to use first their arquebusiers while mounted, in a manner similar to the cuirassiers' caracole but from a larger distance, and then switch to pistols and swords when the enemy infantry formation becomes disrupted. Ideally, they would be supporting the heavy cuirassier units both through harassment and assisting in assault. However, they seemed to have been considered limited in success as they would refuse to close in. Wallenstein notably disliked them.

Organizationally, these units were somewhat confusing, as they were often counted among infantrymen, with the special note that they had horses and thus had higher pay and were given fodder.

A good source to start is Russ Weigley, The Age of Battles, which deals with the introduction of firearms and how it changed warfare. In very, very brief, cavalry went from a shock arm - the mounted charge preferred by medieval knights - to a scouting and skirmishing arm. As infantry packed into squares of pikemen and musketeers, horse soldiers could do little more than ride around and fire pistols at the mass.