The Warmage is a 3rd Edition D&D core class, originally printed in the Miniatures Handbook, but then carried over to more "general" use in the 3.5 Complete Arcane book.
The background is that, unlike Wizards (who spend a lot of time researching magic and collating data into dusty tomes) or Sorcerers (who wield magic instinctively), the Warmage practices over and over in state-sponsored military academies until the spells become almost like muscle memory for those who drill physically. They can recall spells by rote and training, rather than "feel" or "understanding".
This class behaves like a Sorcerer variant, in that it can spontaneously cast from any spell that it knows. The trade-off is that unlike a Sorcerer, its spells are selected for them and virtually all of them are direct-damage spells and there is no scope to expand that without delving into other classes.
This reliance on destructive spells is a legacy of its original purpose in the Miniature Handbook, where classes were designed for tabletop battles to be added to units of troops, and all it really needed to do was blast opponents away at range.
They also gain armour proficiency, being able to ignore spell failure in light armour to begin with, but gain medium proficiency at 8th level where they can also ignore failure chance.
As the Warmage progresses they learn "Sudden" Metamagic feats, which means they can just add metamagic changes to spells without upping the level of the spell. Though it's only one-per-day, it's a nice enough touch if your group gets in a bind.
The class features do allow the Warmage to learn Wizard/Sorcerer spells not already on their list, but these are restricted to the Evocation School, and pretty much just add more flashy destruction spells. In addition, the first class feature "Warmage Edge" allows the class to add their Intelligence bonus to the hit point damage of any spell they cast. This means that they can outstrip the destructive potential of any other spellcaster. So if your group already has a versatility caster, then the Warmage becomes an excellent addition.
Making it Work
Admittedly, while Warmages can do much of the things that Sorcerers can do, the main difference between them is that Warmages are much more focussed on wrecking things and are simply better at it. Good prestige class options are those that expand the available selection of spells, giving them more versatility.
The Rainbow Servant prestige class is particularly awesome, to the point that once you reach level 10 in the class a Warmage will make most divine casters redundant since they get to add all of the Cleric spell list to the spells available to them as a warmage, which they can cast spontaneously from their increased number of spells-per-day. A build including starting levels of Warmage and Rainbow Servant has the awesome nickname of RAINBOW WARSNAKE.
5th Edition Strikes Again
Much like how the Favored Soul was reimagined as a possible Sorcerer subclass, 5e brought back the Warmage as a new archetype for the Wizard - which actually makes a lot of sense, seeing as how there's no longer a difference in casting methodologies between sorcerers & wizards and, well, the Warmage's old fluff about being a rigorously trained arcanist better meshes with the wizard's fluff anyway. In contrast to the Evoker, who perfectly fits the old Warmage's focus on crushing foes under barrages of arcane artillery, the 5e Warmage is more of a tanky and tactical wizard, with features bolstering their defenses and some tactical options. They're themed as "dual-school casters", focused on blending the magics of abjuration and evocation; they're not as good at one field as an Abjurer or an Evoker, but they are more versatile.
Originally, the War Magic Tradition appeared in a March 2017 release of Unearthed Arcana, but they made the jump to being official in Xanathar's Guide to Everything.
At level 2, they pick up two features at the same time. Arcane Deflection lets them burn a reaction to getting hit or failing a saving throw by immediately adding +2 to AC or +4 to their check result, which can potentially nullify the failure. The downside to doing this is that it drains magical energy, preventing you from using anything stronger than a Cantrip until the end of your next turn. Tactical Wit, meanwhile, allows them to add their Int modifier to initiative rolls.
At level 6, they gain the Power Surge feature, which is the most heavily changed feature from their original depiction in Unearthed Arcana. Now, every warmage can store a number of Power Surges equal to their Intelligence modifier (minimum of 1) - that said, they can only gain 1 Power Surge per short rest, and completing a long rest resets their Power Surges to 1 even if their Int modifier is higher than that, which is pretty stupid. They gain a Power Surge whenever they successfully use Dispel Magic or Counterspell, so long as they haven't filled up their storage. A warmage can burn a Power Surge when dealing damage with a wizard spell to add bonus Force type damage to the attack, with the amount inflicted being equal to half the warmage's wizard level.
At level 10, they gain the Durable Magic feature, which makes Concentration spells more viable: whilst concentrating, they gain a +2 bonus to AC and to all saving throws.
Finally, at level 14, they gain the Deflecting Shroud, which pumps up their Arcane Deflection. Now, whenever they do it, up to 3 enemies they designate within a 60ft radius also take Force damage equal to half the Warmage's level.