I love Avalon Hill's games because of the balance and complexity they design into them, and AOR is definitely one of the best. (I hope Hasbro will continue that tradition, but I'm not holding my breath.) With that, I wouldn't start a new gamer on this game, but anybody who's gamed before will love the torture of trying to balance the need to buy advancements with the need to expand.
I think this game is a better version (2.0) of Civilization. You don't get commodity cards for each city you own as in Civ, but rather particular provinces produce certain commodities, e.g. provinces in the far east produce 'spice' or 'silk' etc. For me, this is more interesting, since you need to take over a province economically to acquire that commodity. And as in Civ, when you have more of one commodity, the amount of money you get goes up exponentially.
Others have explained the general game well, so I won't rehash that. In all honesty, there is too much to talk about to do the game justice. To give you an idea of how many facets there are to the game, it typically takes me 45 minutes to an hour to explain the rules to a new player. But it is well worth it.
The commodity log is abysmal. Shame on AH for not testing that more. We don't even use it. Search on the web for documents someone has created which have a small square for each province so you can just take the square when you take over the province. Lose one, give it to whoever took it over. Need to know how many wine provinces you have, count them up in front of you--very easy. In fact, I've heard the next edition of AOR--the European version, I think--incorporates that method into the new design and removes the commodity log.
One bad part of the game is the constant starting point. It always seems you know what Genoa, Barcelona and Venice will do in the first three turns of the game. But as we play more, it becomes fun to try to experiment with different strategies, and I think there may be revelations in future just when you've think you've hit a wall in strategy. That's happened to me in [page scan/se=0431/sf=category/fi=stockall.asc/ml=20]Axis & Allies as well. The whole dynamics of a game can change if someone just does something a little different. Do the same thing... you get stagnation.
All in all, excellent game which our group just loves to play.