AE is the creation of Cryptic Comet, a one-man development studio that has since released a number of other games, and is currently working on a dungeon crawler called The Occult Chronicles. You can download a demo of AE, and I heartily recommend you do, but I also recommend you read the manual or some tutorials before you get started.
The game is set in a post-apocalyptic nuclear desert contested by four factions: the Machine Empire (evil robots), the Xenopods (evil aliens), the Free Mutants and the Empire of Man. You can play as any of them, and they have a nice variety of strategy. It's a genuinely hard game, so don't expect to win your first few tries.
You start the game with a single base on a hex on the edge of the map. This base gives you a steady level of income of the game's four resources: humans, materials, energy and technology. You also start out with a number of cards in your hand, representing units, heroes, bases and buildings available for construction. To bring these things into the game, you drag them on a suitable hex and pay the cost for their deployment. This also includes a cost in action points, of which you only have a limited number each turn.
Initially, I found the idea of having virtual cards kind of silly, but it works well to show the scarcity in this world: you only have a limited number of things you can use, and once lost, they are gone forever. And you don't always have the cards you want, and have to make do with what you have.
So you deploy some scouts and go in search of more resources, and try to find out where the enemy is located. The game is unforgiving: leave your home base undefended for too long, and it is sure to be overrun. This is where the game shines: each decision you make matters. You have limited cards, few resources and only some action points. You must spend them effectively to win. You must balance offense and defense, risk and reward. You can't turtle in your base and let your enemies grab all the resources on the map, nor can you spread yourself too thinly.
At the start of each turn, you and the other two players roll dice to see who gets to go first, and with how many action points. You can spend resources to get extra dice, and at times you will spend vast amounts, because being able to move first can mean the difference between victory and death.
AE is a very deep game: there are over a hundred units, and many special things hidden in the desert. You can also create your own card decks, choosing different strategies, making it even more replayable. Each unit has its own digitally painted artwork, preventing the common problem of wargames looking like an uninspiring mess of stats and icons.
Still, it's not for everyone: it's slow, it has perhaps too many mechanics, and a confusing user interface that often doesn't let you back out of or cancel your actions. A slightly "lite" version of this game would be amazing. I feel that if it were a little bit more accessible and polished, it would be an unmitigated triumph. But perhaps it would be a commercial failure: in the end, it is a hex-based wargame, and I don't know how big a market there can be for such a thing, even when it is genuinely deep and engaging and flavorful.