Hello I am Karechta

This is my Gidlane build that I use when playing Gideon.

Crest

Soulbearer gives you a Shield and Magical Lifesteal, which allows you to even attack the ADC. I Suggest using it while using the Ultimate.

Items

Megacosm

Megacosm allows you to make a lot of Damage early, just casually poke your opponent and deal 5% of their HP by default.
Gideons Passive also deals DOT, when hitting an enemy with a Basic attack after hitting an Ability. This makes for some good Poke Damage.

Caustica

Caustica allows you to spam your abilities, since it gives you a lot of Mana Regeneration. Additionally your Magic Pen increases by 20% of the Enemies Magic Armor, plus another 20% if your mana is above 50%.

Wraith Leggings

Wraith Leggings gives decent Magic Pen and makes finishing off Heroes easier. Can be swapped for Truesilver Bracelet if playing against a lot of CC.

World Breaker

World Breaker gives you a decent Increase in your Magical Power when hitting Enemy Heroes with your Abilities. Stacking up to 5 Times this is perfect for Gideons Ultimate in Teamfights. Maxed Stacks give you up to 20% increased Magical Damage.
As an Addition to that you gain Magical Power based on your MAX HP. This compensates a part of the lost Magic Power if playing Truesilver Bracelet instead of Wraith Leggings.

Oblivion Crown

Huge Damage Boost, gives 120 Magic Power and increases your Magic power by an Additional 35%. Can be bought before World Breaker.

Extra

The resulting Magical Power with all the Item Effects taken into account is around 620. Using World Breaker this increases by up to 20%, being 124 magical power.

I dont use Truesilver Bracelet, since my ult is not my main source of Damage. I use it sometimes, but poking some tanks is very fun with Q.

Play as you like, you can switch the order and Items how you like. Switching World Breaker for Combustion is an Option for Early Game, which can be bought before Caustica. Swapping Combustion with World Breaker is suggested.
Buying Azure Core early is also an Option, which can be later swapped by Caustica.
While Azure Core and Astral Catalyst give a lot of Ability Haste, my build focuses on Bursting the Enemies with the Ult, or the Q.