Welcome to my build for Jayce! He is an exceptionally fun and powerful champion to play with, with endless combos!

(Note: His artwork has not yet been uploaded to MOBAFIRE yet, so it'll stay blank for now).

Pros:

Jayce is very fun to play with.
Powerful Combos make him a MUST as an ally!
Great at turret diving or sniping low HP opponents off from afar.
As a new champion people don't know that much about him if they don't own him (this is to your advantage)!

Cons:

Can be very squishy with certain builds.
Often targeted in team fights due to your enemy's fear of him.
May have some Mana issues if you cast too many abilities in one go.

Runes!

Due to Jayce being predominately AD based, you'll want to stack up on runes like Greater Mark of Attack Damage x9 for your Marks.

Since he is quite squishy if you go for full AD, you will need to take Greater Glyph of Magic Resist x5 and Greater Glyph of Armor x4 for your Glyphs.

I also recommend taking some more magic resist and armour runes for your seals too, such as Greater Seal of Magic Resist x2 and Greater Seal of Armor x2, but you should also take some mana runes too such as Greater Seal of Mana x3 and Greater Seal of Knowledge x2.

For your Quintessences, I recommend Greater Quintessence of Attack Damage x2 and Greater Quintessence of Mana.

The only viable spells for Jayce in my opinion is Flash and Ignite or Exhaust, which allows him to secure kills.

For the masteries, you'll want to go full AD but with the remaining points get some good Magic Resist and Armour.

The items you want to look for are AD and Magic Resist/Armour, and maybe a Mana item or two if you are in need of more mana.

The game recommends Doran's Blade, Sheen, Trinity Force, Wit's End, Aegis of the Legion and Mercury's Treads.

I will choose to support this build but I would not take Aegis of the Legion, to do decent damage with your basic attacks you'll need to buy some AD items.

I would go with the same as the game's suggestion except get Bloodthirster instead of Aegis of the Legion, your team's support or tank can supply the aura for that item.

If your gameplay style demands Mana, you'll need to replace Sheen with another mana item.

You automatically get his transform ability at level 1, which you can activate at no Mana cost. Please note that when you switch to the either form, your first attack will lower their Magic Resist and Armour for a few seconds, meaning that switching constantly will be to your advantage.

Mercury Hammer Abilities:

To the Skies! is very useful for pursuing and killing enemies that are running. To the Skies! is very much the same as Jax's Leaping Strike, except that it also slows the enemy it hits and enemies within a small radius.

Lightening Field passively restores mana on hit, and while active it will create a field of lightening around Jayce, damaging all nearby enemies for several seconds. This is useful in teamfights and sometimes when farming (see farming further down the guide).

Thundering Blow deals great Magic Damage but also knocks your target back, so be careful when using it and don't accidentally knock them back to their turret!

Ultimate: Mercury Cannon will transform your Hammer into a Cannon, giving you new abilities and become a ranged champion. Please remember that every time you cast Mercury Cannon or Mercury Hammer, your passive activates and gives you +40 Movement Speed and allows Jayce to ignore unit collision for 1.25 seconds, making it a great escape tool.

Mercury Cannon Abilities

Shock Blast shoots a ball of electricity in the path of your choice, detonating when it hits your opponent or reaches the end of its path, dealing Physical Damage to all enemies in the area of its explosion.

Hyper Charge increases Jayce's attack speed to maximum for several seconds.

Acceleration Gate opens up a gate which will increase the speed of all allies who pass through it. If Shock Blast is shot through it then its speed, damage and range will be increased.

Mercury Cannon will transform your Cannon back into his hammer.

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I prefer to farm minions from afar, using his Mercury Cannon.

I would start by levelling To the skies!/Shock Blast first, to maximize your damage early game.

After that you should decide what you need most: damage or mana. If you need Mana more than Damage, level up Lightening Field/Hyper Charge, because the Hammer's passive will restore mana per hit.

If you need more damage than mana, then level up Thundering Blow/Acceleration Gate.

That's all I have to say for now, I will update soon with the masteries/summoner spells and whatever when MOBAFIRE put Jayce up.

I hope I helped, thanks for reading!