Disclaimer: This is my first build, so disregard the slight grammatical errors and feel free to criticize my build. Also do not down vote my build because of trolling or other builds. Thank you and I hope you learn something from my build.

The purpose of maxing Titan's Wrath is for quickly clearing the jungle. Then maxing out Riptide second because it is the second most damaging ability Nautilus has and also contains a slow. At levels 6,11, and 16 you max out your Depth Charge of course. Finally, you max out your Dredge Line last because it still fulfills its purpose at level one.
Optional: At level 3 the decision between Dredge Line and Titan's Wrath depends on how you play Nautilus as a jungler. If you plan on clearing your jungle quickly, as in getting blue and red before ganking, then get Titan's Wrath; however, if you plan on ganking early feel free to get Dredge Line.

- Nautilus's passive is what makes him a great disruptor and tank. Staggering Blow has the potential of interrupting ultimates that may wipe out your team in fights such as Katarina's Death Lotus, Nunu & Willump's Absolute Zero, etc. In addition, this ability can also protect your carries by preventing the enemy team from focusing them.
Titan's Wrath is one of Nautilus's primary abilities in tanking and damage. The fact that the durability of the shield depends on Nautilus's health means that Warmog's Armor and Randuin's Omen greatly contributes towards your role as a tank.
Riptide's unique slow and damage allows Nautilus to lock down enemies when he is ganking or protecting his carries in team fights. Synergizing with Dredge Line, Staggering Blow, and Riptide absolutely cripples a champion and forces them to flash or evade like Maokai's Twisted Advance. Therefore, Riptide should be maxed out after Titan's Wrath.
Similar to Blitzcrank's Rocket Grab, Nautilus's Dredge Line is an excellent tool for initiation and disruption since it can interrupt channeled ultimates such as Karthas's Requiem, Shen's Stand United, etc.
- Great ultimate since it can knock up enemies as it travels towards the targeted champion. Another ability that can disrupt.

For ganks and initiations from a distance:

- is a wonderful summoner spell overall, mainly because it has the ability to be used in initiations, kite/baiting champions into killing you because your low (surprise Titan's Wrath, or fleeing from team fights when you are critically low in order to not feed the enemy team.
- Your a jungler.
Teleport- Not needed at any time.
Clarity- Not needed since you have philosopher's stone and/or blue buff.
Ignite- Optional if you want to ks your teamates
Exhaust- Optional: pretty good in ganks, but Nautilus has enough cc that it is not needed.
Ghost- Not needed if you have Mobility Boots, Force of Nature, or any other boots.

Defensive Tree:

• Summoner's Resolve - The bonus gold from smite makes is nice since your gonna be using it often.
• Hardiness - The armor will help you in clearing the jungle and ganks.
• Tough Skin - allows you to take less damage when clearing the jungle
• Bladed Armor - helps in killing creeps
• Durability - The extra health is useful especially in tanking.
• Enlightenment - Cooldown reduction is fantastic on Nautilus, that way you can spam your abilities.
• Initiator - need this mastery for good mobility throughout the entire game.
• Honor Guard - Its a nice mastery point for tanking.
• Juggernaut - Good for durability.

Utility Tree:

• Summoner's Insight - Good for flash
• Expanded Mind - More mana is nice for Nautilus, since he can mana starve himself if you are new to him.
• Swiftness - Nautilus needs the movement speed.
• Runic Affinity - good for jungling

Greater Quintessence of Movement Speed- Nautilus needs this for his ganks and because of his slow base movement. It is literally 300 movement speed which is equivalent to Ashe.
Greater Mark of Attack Speed- The same goes for the majority of the junglers in leagues, Nautilus needs it for clearing minion camps and it helps with Titan's Wrath.
Greater Seal of Armor- bonus armor is good for clearing minion camps and helps in team fights.
Greater Glyph of Scaling Magic Resist- need the magic resist per level.

Optional:
Greater Seal of Vitality- if you feel that Nautilus is too squishy, feel free to get this.
Greater Quintessence of Ability Power- if you do not have movement speed quints, these are adequate at jungling.
Greater Quintessence of Health- bonus health is nice.

Standard build:

• Mobility Boots- need this item for ganks and to compensate for his slow movement speed.
• Force of Nature- great item because of the movement speed and the magic resist it offers.
• Warmog's Armor- Nautilus needs this for his Titan's Wrath and to become beefy.
• Randuin's Omen- The passive is simply amazing like a better version of Thornmail and the active is practically an AOE exhaust.
• Frozen Heart- Great passive and the cooldown reduction is simply great for Nautilus's abilities.
• Abyssal Mask- Good magic resistance, magic resistance debuff, and allows you to do damage.

Optional Items:

• Aegis of the Legion- great item if you are not the main tank of the team, you can get this after getting heart of gold.
• [Banshees Veil]]- Good magic resistance, mana, and health bonuses, but Warmog's Armor, Frozen Heart, and Force of Nature already give these bonuses.
• Rod of Ages- Good item for damaging and tanking item.
• Shurelyas Reverie- decent item, but your support is most likely going to get this item.
• Guardian Angel- great item if you are always dying in team fights.
• Sunfire Aegis- decent
• Thornmail- Great item if you are going against a team with a ridiculous amount of auto attacks.

Jungle Routes:
1. Do wolves with the help of nearby lanes at 1:40
2. At 1:55 your mid should leash blue golem and the nearby lanes(as in top or bot lane) should damage golem till it is like 500-600 health.
3. Do wraiths after blue golems.
4. Do wolves again
5. Go get red buff
6. Get golems
7. Gank
8. Recall

As you can see throughout the guide, Nautilus's crowd control compensates for his slow movement speed. Overall, Nautilus can contribute a lot to his team as long as your team is willing to cooperate.