Superman The man of steel is one of my favourite characters to play on this game. His skill kit is really fun and he's a great character all around.

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STOLEN POWERS

[[Superman's Super Strength]] - it gives you an AOE/Knock-up attack and while on cooldown you get extra attack damage.
[[Poison Ivy's Healing Wave]] - I find myself using this more than Invurnerability shields recently, not only does this also help your teammates, you also get a short damage buff.
[[Doomsday's Invulnerability]] - the health shield you'll need to help you in a tight spot.
[[Flash's Super Speed]] - for a quick getaway or chasing.

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SKILLS

 KRYPTONIAN MIGHT (Q)
Superman's main attack skill boosts his next basic attack. You get max 2 charges to use it and generate 1 charge every 8 seconds. Use this right after your normal basic attack to do a quick 2-hit combo.

As the damage increase is not much when leveling up, it's better to leave this as the 3rd skill to level up.

FROST BREATH (W)
Use the slow and root to stop both fleeing and attack enemies, while you either reposition yourself, or just pound them alone or with your allies. You can also, of course, use it to help you escape as well.

Scales with Power Damage rather than Attack Damage, but it can still deal a good amount of damage, enough to finish off a target or at least slow him to get to him.

The reduced cooldown when leveling is well worth leveling this skill as soon as possible, as well as the damage.

HEAT VISION (E)
This is the most fun skill to use out of all of Supermans skills. The initial attack pushes the target away and reveals them for 2.5 seconds. While revealed, you can activate this skill again to jump to your target, dealing more damage.

You can use the push to reposition and single out enemies, you can also blast those who are using attacks that take some time to complete (like Nightmare Batman or Mecha Wonder Woman ultimates. This will push them away, ending their attacks early. You can also use it to help you or your teammates escape, by pushing a chaser away from you.

However, when chasing be aware of when to use this skill, as it will push enemies way from your teammates so you'll have to use frost breath to give them a chance to cath up. You shouldn't use this when chasing an enemy if you don't have Frost Breath ready, as you'll only help the enemy escape. Even better if you have [[Lobo's Chain (4)]] hook shot ready when using Heat Vision, this way you will make it nearly imposible to escape and an almost guaranteed kill.

In fact, some enemies like to use their escape skills as soon as you push them away, thinking they're getting a good distance between you.

Use Heat Vision (E), follow with a basic attack and Kryptonian Might (Q) right after, then use Frost Breath (W), another basic attack followed by the 2nd Kryptonian Might (Q). Use Hook Shot, if you have it, depending on when the enemy likes to dash, try using this combo once or twice on them and watch when they like use their escape skills.

One more good and fun way to use this is to not jump back on the enemy as soon as you can. Wait a second or 2, give your other skills a chance to go off cooldown if you need/want to, run the other way if there are other enemies nearby or even attack those other enemies. Then when you do jump on the enemy, the rest of their team will stay behind and there will be nothing left in your way to stop you from kill them.

Despite all the fun you can have with this skill, its best to just level it last, you'll probably be using your Q way more than this so it's better to add the damage to it first and just level this last.

SPEEDING BULLET (R)
Supermans most powerful attack. Can be used either to get Superman into a fight to help his teammates and turn the fight around, or to finish off anyone who thinks they escaped, securing the kill.

Obviously you shouldn't use this while there are enemies between you and your target, because they will stop you mid-flight.

Level up every time you can, the damage is worth it, but the lower cooldown time is the best.

MAN OF STEEL (PASSIVE)
While it's off cooldown, every skill Superman uses gives him a shield. It scales with Health, so you'll want to build that as early as you can to get the most use out if this. Level up this 1st or 2nd to get your shield to be useful as soon as you can and you can go on rampages just using this to keep you alive for an extra second or 2 even against the most strongest of foes.

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ITEMS

Starter
[[Lobo's Chain (4)]] helps you stick to your targets. It also gives you a bit of attack damage, but the important effect is the extra health, which really helps early game and adds strength to your passive.
Also getting [[Hawkman's Harness (4)]] whenever you can is a good way to use that money while you can't yet buy what you want to.

Attack Armor
Suit Of Sorrows (4), [[Booster Gold's Power Suit (3)]] and [[Metallo's Heart (3)]] seem to be the best choices on Superman for Attack Armor.
Suit Of Sorrows (4) offers the highest Attack Armor in the game. Get the 25% Reflect mod for this, and you'll be almost unstoppable vs AD Champions.
[[Metallo's Heart (3)]] is the 2nd best choice, offering less Armor than Sorrows but also giving CDR and a debuff aura that can really help both you and your team.
[[Booster Gold's Power Suit (3)]] offers Health, Cooldown Reduction and shields you from turret blasts a bit.
You'll want to grab only one of them, but if your opponent team has high/many attack damage champions, you can build 2.

Power Armor
[[Mirror Master's Prism (4)]] with the 40% Reflect mod of will make you have a nice amount of defence against Power Damage and give turn their own attacks against themselves.
Entropy Aegis (4) and Kryptonian War Armor (4) are also good choices.
Entropy Aegis (4) gives you Health and a Shield to block the next skill that hits you, so it's a really good choice.
On the other hand Kryptonian War Armor (4) gives you health regen and, more importantly, movement speed, which can really help you get as far away as you can when someone starts blasting you.

Attack Damage
Now Superman isn't a tank, you'll want to deal damage as well. Unless you wanna build him full tank (in that case go nuts). Anyway, this is where items such as [[Joe Chill's Revolver (4)]], Velocity 9 Implants (4), [[Deathstroke's Claymore (2)]], [[Lobo's Chain (4)]] and [[Huntress' Crossbow (3)]] come in. Now there is a lot of items to choose from, and just pick ones that go best with your play style, enemy team composition or just what you like.
[[Lobo's Chain (4)]] offers health, some damage and a slow. Great for his passive.
Claw Of Horus (3) gives Attack Damage and Armor as well as health. Great for his passive too.
[[Huntress' Crossbow (3)]] offers a lot of Attack Damage with Attack Speed thrown in too with a great effect too.
[[Joe Chill's Revolver (3)]] offers high Attack Damage and a critical damage boost.
[[Deathstroke's Claymore (4)]] offers damage and cooldown reduction along with penetration and a damage boosting ability.
Velocity 9 Implants (4) and offers Movement Speed, Attack Speed and Critical Strike Chance.

Psi-Scimitar (3) offers both Attack and Power Damage, great to strengthen your forst breath too, as well as empowering your next basic attack, even more so with the modded version.
MINDSET

Superman is an bruiser champion, Meaning you'll want both to be able to take and deal damage. This build will make sure he would be unbeatable 1 vs 1. You'll reflect 25% Attack and Power damage back at your opponent, you'll also have high Attack Damage, thanks to your offensive item set, and medium Armor. Combine that with your crowd control abilities and no one can escape you.

Don't be afraid to use your ultimate to kill those who do escape, it's not just a skill to get you to your team quickly from halfway through the map. It's can both start you a fight and end it. Make sure that its use either secures a kill, or prevents a death and it will never be wasted.