This is my first build so take it easy. Its for the ever so famous "AP Yi". I warn you, this is not as easy as the AD/AS Yi, but can generate some fun results in game. If you know how to play, take care, and just use some common sense, you should be fine. If you have what it takes, Yi is one of the best (AKA Cheap noob stop playing Yi) Champs in the game, and only at 420 IP.

Anything that will give mana, CD reductions and AP works.

For my masteries, I went mainly in Utility for CD reductions and mana boosts. Also, I went in offense for of course, Archmage savvy. I went in the Flash Upgrade in utility because thats what I use, you can do whatever your Summoner Spells are.

I know, I know. Four dorans Rings? Are you crazy? Well, yes kinda. but thats offtopic. The reason I love dorans items, is because the insane boosts they give. It gives you mana per second, 15 ap, and 100 health. this can quickly change the tide of those pesky early game ganks.
Buy four, because thats a quick 60 AP at a low price, with Mana and Health.

After you've bought your fourth, go back and buy boots of speed. You should have 1 slot left. When you have the money, upgrade to Sorcerers Boots. You can Even go in boots of Lucidity if the CD's are bugging you.

Now it depends on how the games going (and usually its going well). If your racking up the kills, listen to this. If your not, skip this paragraph. Buy Amplifying tome, and update into Mejais. Thats a quick 180 Ap, if you can keep up. Keep in mind, thats only for 1220 gold....

(If the games going bad, go straight to this part, and skip the Mejais). now go for the Fiendish codex. It gives you the mana and Ap you need, and quickly build it into morellos evil tome as fast as you can. BTW, you will need to sell one of your pimp rings for this.

If you havent won the game by here, start moving into the Rabadons and Void for the obvious Ap boost. At around this time you will be healing yourself for over 1200 and Alpha will be doing 500+.

Make sure to max out your Alpha and Meditate as fast as you can. Get higlander whenever, and only get Wuju if you need. The Ratio for meditate is crazy high, and its also really good for Alpha making Yi quite good when gone AP STYLE!

Completely up to you. Obviously do not use stupid spells like Revive, Heal Or Clarity. They are a waste of a slot. If you are more team connected, get yourself Teleport. For the master of escape go Flash and Ghost. A variation with Exhaust can be combined. Enjoy your AP YI!

Now you have Items, Spells and whatever else you need (excpet runes...). Now go out there and "wuju" please show them the way of the AP yi!