This is my Cho'Gath build, that has never let me down yet! If you require reasons for my build look below for a more detailed explanation.

I have tried my best to make this guide as good and as detailed as I can for you guys, please let me know if there are any errors, or some things I can improve on as this is my first guide.

Thanks, enjoy!

Starting Items

This is the only way to start Cho'Gath, nothing else works that great if you want to go full AP, also Doran's ring works great with his passive since early game he has a massive mana problems.

First Back

Needlessly Large Rod - If you have 1250+ gold get this item straight away, the raw AP helps a lot in lane.

Aether Wisp - Get this if you have 850 - 1050 gold, if you have 1050+ gold then just go back to lane and save up for when you can get your needlessly large rod.
REMEMBER YOUR WARD. I always try to get 1 green ward on my first back if possible, except if they have an eve jungle then I will get a pink ward, it is worth it to buy wards they WILL save your life

Core Items/Other Options

Luden's Echo - Now is where most of you are probably confused on why I build this item first, most people say buy Rod of Ages first so you can get your stacks quicker blah blah blah, but Cho'Gath does not need the extra health and mana straight away. If you build Luden's when you get to lane people NEVER expect how much damage you will do. A level 6 all in with Cho'Gath will destroy most mid laners when you have ludens. Just silence so they cannot jump away from your knockup, Q them and ult, I assure you they will 9/10 die from this and if they don't just auto a few times and ignite.

Sorcerers Shoes/Mercury Treads - Pretty self explanatory, the extra movement speed to catch up with people and the magic penetration. BUT if there team has a lot of CC then I would recommend buying mercury treads, they may save your life especially if you're vsing a veigar

Rod of Ages - By the time you have bought this item you should be pretty fed, and you will buy Rod of Ages to help you stay alive with the extra health it gives you and the regen every level up, also by now you may be having a lot of mana problems so the mana it gives really helps with that. You also have enough time to get your stacks by roughly 20-30 minutes if you are doing good

Rabadon's Deathcap - What can I say expect this is a MUST go item for every AP mid laner. Would you like some AP with that AP? Yes pls

Zhonya's Hourglass - These last two items can be switched around depending on what you prefer/need at the time. I normally buy Zhonya's first because now it will be getting to the part of the match where you may be getting focused a lot so you need some protection, especially in solo que since you cannot depend on others to save you

Rylai's Crystal Scepter - I get Rylai's last because, its passive combined with your Knock up slow, the enemy will never get away from you again, if you knock someone up at this point they are most certainly dead

Other Options

There are a lot of different options as Cho'Gath that you can build depending on scenarios. These are just a few that seem to work well if you need them

Banshee's Veil - Get banshee's if they have a lot of AP and CC, the banshee's passive may just save your life from some devastating CC

Mejai's Soulstealer - Get Mejai's ONLY when you are doing crazy good, this item can make or break a game and I do not highly recommend it at all. It can just be a great item if you are dominating a game

Liandry's Torment - Get Liandry's if you feel like you need some extra health and magic penetration, I rarely every buy this item because Cho'Gath get's loads of health just of his ult passive so it is never really essential. Other items just tend to work better

I'd only every replace Zhonya's and Rylai's for any of these other items.