I plan to add 3 or 4 more builds for Jayce to this guide including, Mid,Jungle, and also builds for when you are doing bad in those lanes.

First things first, this is not a guide that will make you immediately a professional with Jayce, if you are barely starting to play Jayce (or league of legends), failures from using this build is not my fault but your lack of knowledge on the champion (or game). If you are very familiar with Jayce I am more than happy to hear your words. I don't mean to sound rude, but I need you to understand if you plan to vote. Thanks.

Hey everybody name's Agil, summoner name is 'Bigblackbrotha' G1 (S4) G4 (S5). Starting to mess around with the new items released with S6 and I found a great way to play Jayce without the need for Manamune. I personally always felt that champions who absolutely required Manamune to be played were champions that should not be played.

Rushing the item left you with no health and no real damage, only mana, therefore with Essence Reaver being made I have found a build for Jayce that has worked flawless for me in game. This will be a quick summary of why I picked what I did above. I don't plan to explain things you should already know.

This is a build focused on farming all of early game, to build a strong and steady middle and late game.

Moving on.

Reds: Flat attack damage

Yellows: Flat armor

Blue: Scaling Magic Resist

Quints: Flat attack damage

We want as much Attack Damage as we want to help our early game farming. Defensive Yellows and Blues to help keep us in lane by reducing damage taken from all sources.

The only mastery absolutely needed for this is the Keystone:
Warlord's Bloodlust (Crits heal you for 15% of the damage done and give 20% attack speed for 4 seconds. 2 sec CD)

Essence Reaver gives mana when you crit, this is our main source of regeneration. Paired up with this keystone you will also be healed for 15% of the damage done and also gain a small steroid for a few seconds.

The masteries I highly suggest are:
Feast (Heals for 20 health when you kill a unit. 20 sec CD)
Vampirism (2% lifesteal)
Savagery (Attacks deal 5 bonus damage to Minions/Monsters)
Mediation (Restores 1.5% of your mana every 5 seconds)

Once again this is all to help us stay in lane longer to farm more minions.

Max To the skies!/Shock Blast (Q) first. It's the move that scales the best for early game, allows you to poke from far away for good damage or secure creeps.

Secondly you Max your next skill based on your opponent.

Max W vs Ranged/Non gap closing champions. If you opponent lacks a gap closer or is ranged you will want to max Lightning field/Hyper charge. Hyper charge does much better at trading damage with ranged champions than your E would.

Max E vs Tanks/Gap closers. You want to max your Acceleration gate/Thundering Blow vs Tanks and gap closers because your Thundering blow knocks targeted enemies back and it does % magic damage based on their max health. This is good to punish those who think you are weak when melee.

This was a guide for those who know their way around league of legends and isn't exactly tailored for new players (under level 30). Reasons why I didn't explain my summoner spells or what each move does exactly is because you should know why I picked Flash/TP and you can look up the details of Jayce's abilities anywhere. Most details I left out are not details on how to play Jayce but details on how to play the game which you should or will learn as you play more games.

If you are not good with farming, this is not the guide for you. Look up some farming videos, there are fantastic videos out there which I myself have learned to farm well through them.