Where and when to use this build?
This build is meant for solo top 3's position. As reason of this is the only place I tested the build in. I DO NOT reccomned this build for dominion or 5's because it hasent been tested.

Why an ap build?
I have tested countless times this Nautilus build, each in different lanes and the best to work with is top lane. If your team isnt expecting you to play nautilus as an ap fighter then this build is not for you. Yet this build make Nautilus a formitable top laner as his Dredge line has quite the distance to prevent issues with ranged and yet the utility of pulling out of an unsafe melee combatant's range. Secondly, all of Nautilus' abilities stack ap so we want to get some damage rolling on this guy, after all were not in top to tank were here to find the convicted. (Nautilus move quote/saying)

Since this build utilises the heavy ap stack Nautilus naturally has were going to tweak into his ap role, almost like a Mordekaiser he will be able to sustain himself due to Titan's Wrath granting a shield based stacked off of ap.

Starting with the Marks I pick the standard magic penetration to increase effectiveness of building the ap. Other wise you will have the ap but no penetration to back up your damage, therefore not being as effective.

With Seals I prefer armor, in masteries you can see i already spec'd into hardiness. We don't want Nautilus to appear scary and have no bite to his bark so to say. So flat armor seals is the way I went.

Not buying ap items till the 3rd item takes a toll on our damage concidering we have already decided were not tanking to not have any damage or tankyness would be silly, hence the Glyphs of force. As a skilled player I level up to 18 fast in game so its fast payoff for the level incrememted ap stack opposed to flat ap. This gives us a constant flow of increasing ap so no matter what items we buy at least were leveling and always gaining more dmg source.

Quintessences from my perspective should always be further increasing a stat we already chose instead of staying too thin in our buffs, the added ap per level is such a boost and to just bring the magic penetration up to 10 really helps with early game damage. This relates to the sorcerer's shoes being the main priority, as in early game we now have arround 30% penetration which will be where we stay the rest of the game.

Basic all heavy ap dmg build. Straight down the ap side of the offence table.

You going to be a mean team mate but you will be helping them long run. Always go to your teams pings and ganks, help them kill buffs but do not take them, were not in this for the prizes only redemption. So whenever you get the chance always steal champion kills but leave the minions and monsters to team mates. Gotta share one thing or the other.

The range on Dredge Line is nice but wouldn't it be nicer to catch up to the enemies to use it? Well correct, we want our first abiity to help or cause and team by bringing in the baddies and doing it efficiently. So we grab a boots of speed, i don't want to get repetative but I said before we get sorcerer's shoes early game and i meant it, we are now at ramming speed and catching those enemies with our anchor. In addition to the magic pen.

Our next item aimed to be is Will of the Ancients, stacking fast and cheap ap is always a plus but we gain some spell vamp while were at it.

Rylai's Crystal Septer works hand in hand with Nautilus' passive it gives some extra chance to prevent enemies from getting away from his activated Titan's Wrath. At this item we have health some armor going on from our abilities , were mobile and starting to hit hard and be scarry.

Depending whether or not your going up against other ap champions some magic resist is always usefull. With at the same point Nautilu's oceam of mana may seem to be drying up fast. Our solution is to buld an item with a variety of purposes and we find Lich Bane. Why we need this item right now and how is it so usefull? One it gives us mana, two we have some magic resist, three more ap look at that! The one major reason is the Unique passive of Lich Bane. With having so much ap and having a melee champon, comboed with Dredge Line and Staggering Blow, we now are almost doubling the purpose/damage out put of Dredge Line. By adding all of or ap into that instant auto attack Nautilus will land on your target.

Rabadons Deathcap makes us crazy levels of ap furthuring the power of our anchor ability which has become our bread and butter move.

Zhonya's Hourglass solidifies a wonderfull cap to our ap ussage yet gives a shiny tanky feeling to this heavily armored scubadiver. Even Gragas would be jelly of our suit of scuba gear.