Enchantment: Runeglaive changes the entire way ap gp operates, and it's all down to one simple difference between how Enchantment: Runeglaive and Lich Bane do damage. You see, Lich Bane adds a chunk of magic damage onto your initial attack. This damage is seperate to the attacks base damage and as such is unaffected by attack modifiers. Enchantment: Runeglaive on the other hand converts your physical attack into a magic attack with a modifier causing it to do bonus damage (based on your base damage and AP). What this difference means is that you can now do magic damage that crits (and benefits from spell penetration). This completely swings ap gangplank from being an off-meta normal game pick, to actually being outright better than regular critplank just because of how fundamentally it changes Gangplank's interactions with the rest of the items in his build.

If you wish for me to elaborate further, well here's the guide :)

MID: Ap gangplank is a solid counterpick mid against champions that use a cc to launch the rest of their combo ( Malzahar, Morgana, Ryze, Swain, Anivia). He isn't as effective against champs with multiple cc's however as they'll often wait for you to w off their first cc before launching their 2nd attack. Champions which rely on their burst damage ( Talon, Fizz, Katarina, Akali) can also become much stronger than gangplank at level 6, as you'll no longer have the ability to sustain all of their damage. However these tend to be delicate early on, and can be harassed away from farm.

TOP: Ap gangplanks early game is essentially a more passive version of how he would normally be played. Gapclosers with stuns are his anti-matter if the enemy has ood followup damage ( Jax and Xin Zhao). While characters that are weak early -Particularly melee- (eg. Tryndamere) can be pushed away with your harass and allow you to be more aggressive in lane (junglers not residing). Enemies that rely on harass vary in difficulty.

-Always take into account your allies choice of champions when choosing your own-

Clairvoyance
You may be thinking, "Oh wait if I use Clairvoyance I can hit anyone on the map with Cannon Barrage" and this may be true...the first time you use it. After that however it just becomes a giant warning that your ults coming along. +You're not support. +There's a trinket for this numnuts.
Clarity
If you don't like the health and mana pot start, this will make your early game sustain better, however I find it be less useful late game than the other summoner spells. (Also it doesn't exist anymore)
Revive
Used to be good on karthus. But now it no longer exists. So if you have this, you're either really dedicated to not changing it, have hacked your LOL client or have traveled to the past.If its option number 3, you clearly know something I don't.

Jungle
If you wanna jungle, just grab this and a couple of pots. Not much else to say on this right now.

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Sustain and Safety
A strong farm and sustain orientated start. With a couple of red/blue pots it'll be pretty hard to force Gangplank out of lane.

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Anti-Ad
If your lane opponent seems particularly aggresive, you wouldn't be remiss in picking up some armor and a bunch of pots to prevent yourself from getting burst down immediately.

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Sheen rush
You can buy either sapphire crystal or faerie charm if you're confident you won't get wrecked by your opponent. Faerie Charm lets you get more potions but doesn't provide the same mana that Sapphire Crystal does early on.

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Enchantment: RuneGlaive
So I already explained the 2 MAIN reasons this item is great (the bonus damage can crit, Parrrley now does magic damage that benefits from spell penetration). But there are other benefits to this item that make it just as, if not more so, ridiculous than Trinity Force. Firstly, it provides cooldown reduction, one of the strongest stats in the game for GP thanks to his ultimate. It provides a hefty chunk of AP and mana greatly increasing his sustain. It also shores up Gp's mana problems with the 8% mana recovery passive. Finally it does its damage in an aoe, meaning it gives Gangplank a means of wave clearing quickly as well as hurting multiple targets in a teamfight. Oh and the bonus damage actually scales with ap and crit damage, as opposed to being binary. Also Trinity Force is one thousand, five hundred gold more expensive than this item. + Skirmisher's Sabre is crazy good for skirmishes (DO YOU GET THE JOKE??, I MADE A FUNNY!!).

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Statikk shiv
If you just skipped to this item to see why it's in this build here's why: Runeglaive damage can crit. Ergo it benefits from crit chance. The power spike this item gives mid game will have you critting for nearly a thousand damage without other items. The passive effect benefits from magic penetration so it scales decently until you've hit 6 items. Bonus points for extra movespeed, attack damage and one of the quickest-smoothest item buildups of any item in the game. This right here is crazy good. Build Avarice Blade first if laning, Zeal first if in the jungle.

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Nashor's tooth
The straight damage option. This provides better auto trading and pushing power, but lacks mana sustain when compared to the alternatives. That being said it's a very solid option when ahead, as it'll compound both your dps and ultimate presence greatly.

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Morellonomicon
Slightly weaker when trading, but gives mana and a circumstantially powerful passive to compensate. If you're against heavy health regen, this could be the item to go for.

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Athene's Unholy Grail
Like Morellonomicon, but with a leaning towards Magic defense. Ergo its good versus magic. Duh.

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Rabadon's deathcap
Lots of AP means more heals and more cannonballs. It also scales your Parrrley procs up nicely. Good for when you want a bit more from all of your abilities.

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void staff
Parrrley scales with penetration now, so this is a much better option than it formerly was. Less healing than Rabadon's Deathcap, but your Cannon Barrages and Parrrleys will hit like trucks.

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Infinity Edge
Crit with Parrrley and remember the good old days. You'll still be doing magic damage on Parrrley, but now your physical attacks won't be anything to sneeze at. This'll make you harder to itemize against as the game goes on. If you get into the endgame without picking this up,use it replace Statikk Shiv.

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Liandry's torment
Gives solid magic penetration and an awesome passive for your ult (if it works on Parrrley still, that's a bug they'll be removing next patch). It also gives a decent chunk of health. Good against tanks, not much else.

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Luden's echo
Like Liandry's Torment the passive working on Parrrley was a bug. That being said this is really only good for replacing boots during endgame thanks to the MS it provides. If the bug still exists, then go nuts.

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Abyssal Scepter
Way better now that Parrrley is magic damage. Since we already have a bunch of CDR the stats and passive on this are well worth the cost. Gives survivability while not forsaking damage.

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Sunfire cape
Synergizes well with Abyssal Masks aura and the two combined make for a solid defense. It also benefits from other magic penetration sources and gives a bit of health making it a good generic defense option.

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Get these at some stage, preferably early on. Sorcerer's Shoes are the straight damage option, not worth finishing though until you have Enchantment: Runeglaive. Ninja Tabi will help you deal with ad opponents. Mercury's Treads are good for dealing with lots of magic or crowd control effects. Finally, Ionian Boots of Lucidity work only when you want to go full damage items without CDR, so I wouldn't recommend them myself, but whatever works for you.

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V All dat heal :3 V (from HeadinPants)