Galio is my new favorite champion. He is extremely tanky, carries hard, and does tons of damage late game while having full tank stats. This guide won't be super detailed; however i am writing it to share my ideas that i don't agree with in other builds, specifically with runes, masteries, and item choice/order. with this guide, you will have the mana regen to spam your Q a ton, and just simply out harass and sustain your enemy, reducing their farm.
Also JunGlio, pretty cool guy indeed

Pros:
- fun to play
- lots of utiliy
- farms well
- AoE taunt
- AoE slow, movespeed
- harasses like a boss
- can out sustain almost any other mid laner
- high burst damage

Cons:
- abyssal scepter and fiddle lower your AP
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9 x Greater Mark of Insight: Magic pen is magic pen. what else to say?

4 x Greater Seal of Replenishment/5 x Greater Seal of Clarity: 4/5 is best on Galio for mana regen, as he is very mana hungry early and mid game. If you compare it with 9 replenishment seals, it gives 1 less regen at level 1 but ~the same at level 6, with at levels 7+ you get more regen from the per/lvl seals. i also don't go with 9x clarity because galio still needs that mana regen from level 1-6, which is when galio is even more mana hungry.

4 x Greater Glyph of Warding/5 x Greater Glyph of Shielding: Basically the same reasoning with mana regen, however compared with 9 x shielding you have 6 more MR at level 1, and 5 less MR at level 18. the 3 extra AP and MR is more important early game than the 2.5 AP and 5 MR late game, imo. also with warding you start out with 6 extra AP and 13 Mr, however, you loose ~20 MR and 10 AP late game, which is not worth it imo.

3 x Greater Quintessence of Fortitude: with quints and masteries you have an extra 114 HP at level 1. pretty OP.

Optional: 3 x Greater Quintessence of Potency: that extra 15 AP at level one along with your MR you will be hitting hard with your Q. I sometimes run these mid over HP quints, to deny the enemy AP carry early game. Squishier they are, the more of these you should run.

Masteries are one thing i disagree with most with other people on Galio.

9/9/12 is what i think the best mastery setup for Galio. It gives him some AP, CDR, magic pen, defense, HP, much needed movespeed, and more mana regen to spam spam spam your Q early game.

The Required:

- Flash: needed on galio to initate with his ultimate

The Good:

- Exhaust: very useful for receiving ganks, generally good all around. take this if no one else has it
- Teleport: very good for solotop (teleport down to dragon fights and wtfhax poop on everyhting)
- Ignite: a very good skill in general to add you your burst damage
- Clairvoyance: - a very good pick for galio if your support doesn't take it or you don't have one. take it if no one else has it, as Galio essentially has a free summoner slot.

The OK:
- Heal: used it once, was nice to use after i ultimate to increase survivability
- Clarity: we have mana regen, we don't need this. good for beginners though.
- Cleanse: don't like CC?

The Bad: everything else.

Most people who play Galio max out his Q first, then don't know whether to max W or E next. survivability, or damage? really, it is best to max BOTH at the SAME TIME. if you max one over the other, your either really squishy or your E deals no damage.. if you balance it, you have a good balance between damage and survivability.

Couple of notes:
- AP is built more towards late game, as if built earlier it hampers your tankyness.
- Thornmail, while cheap, doesnt do as much damage as people think and really doesnt fit into this build.
- doesnt build full traditional tank, this Galio build has some useful auras and abuses passives to survive (GA, BV, ZH)
- with this build you will be extremely tanky and over 300 AP to boot.
- ALWAYS BUY WARDS! everytime you go back, make sure you buy atleast 1 to 2 wards, it will help you and your team out a TON


Early game:

Null magic mantle+2 pots: get this item to boost your AP and MR early game

Mana chalice: gives Galio the mana he needs and build off null magic mantle

boots: boots. nuff' said

Catalyst the Protector: some needed HP and Mana early game, amazing in order to out-sustain any deny your opponent even more.

Mercury's Treads: more MR and level 2 boots, and tenacity a need to have in current meta


Mid Game:

Spirit's Visage: A VERY underrated item on galio, it gives all what he needs: HP, MR, CDR, and the increase on your regen/healing from W is just a bonus

Aegis of the Legion: A very cheap item for lots of HP, MR, and some now much needed armor. Also comes with a great team aura, and team fights start to occur around this time.

Chain Vest: LOTS of Galios tend to build little armor early and mid game, mainly due to his passive. however, unless the enemy team is all AP, you will die super fast without this much needed boost in armor. Also, you cant not build armor and use your W as an excuse, it only lasts 4 seconds and still isnt enough at this level.

Guardian Angel: More Armor, some MR, and the passive is always nice if you die too early in teamfights due to your ultimate.
Oracle's Elixer: at this point it is best if you carry Oracles, as you rarely die with W+GA.


Late Game:

Banshee's Veil: Time to upgrade your catalyst, and get some MR to boot. Very nice passive to protect your ultimate form interrupting, especially against someone like Leona for example.

Abyssal Scepter: Sell your Mana Chalice and buy this bad boy. now you can start to build that AP we talked about. comes with some yummy MR.

Zhonya's Hourglass: sell your Spirit Visage before buying the Chain Vest, as more armor is needed at this point in the game. Nice AP bonus and amazing passive.

AP Galio: quick overview

Mana Chalice: mana sustain to spam your skills to hell
boots: boots
Hextech Revolver: i think this is an extremely strong item on AP Galio, you can never force him out of lane with this.
Catalyst: even more F**king sustain! farm forever and never die with this+hextech revolver
Sorcerer Boots: boots+pen!
RoA: HP, Mana, and AP
WotA: AP, nice aura, more spellvamp
Deathcap: more damage is needed at this point
Abyssal Scepter: AP, MR, AP, why the hell not?!?!?!?
Zhonyas: much needed armor, loads of AP, nice passive (to lol survive after ultimate)

If you want Void Staff:
replace sorcerer boots with mercs, and take out abyssal scepter. Magic pen and magic % pen do not mix.

Jungle Galio is very fun to play

Pros:
- very fast clear
- tons of sustain from his shield
- very good ganks, lots of burst damage
- unexpected pick, not easily countered
- counter jungles enemies smaller camps extremely well, sorta like chogath
- resilient to counter jungling.
- at dragon/baron, can use flash->ulti to taunt enemy jungler for an easy steal
- nice level 2 ganks
- travels fast in jungle due to your E
- lots of aura items, still very tanky
- VERY cheap build

cons:
- relies on blue buff early game
- doesn't use red buff well
- not enough farm in jungle for Galio
- can't contest dragon as well as bruiser junglers or someone like cho or nunu
- less damage than AP tank Galio

Route: get your mid/solotop for blue team or bot/mid to help with wolves, get mid to pull blue. so:

wolves
blue buff
Gank (if you took E) or go to wraiths if you took W
double golems
red
wraiths
gank Mid, recall, or go to wolves then recall.

Summoner spells:

Flash: needed to initate
Smite: must for junglers in general

items:

early game:

- Regrowth Pendant+ Pot: because Jungler Galio doesn't get as much farm, we rush GP5 items
- Philo stone: regens and GP5
- boots: boots
- HoG: HP+ GP5.
- Mercs: MR, Tenacity, level 2 boots!

Mid game:

- Catalyst: more HP+mana, builds into banshees
- Spirit Visage: HP, MR, CDR, and more sustain in jungle from W
- Banshee's Veil: MR, shield to prevent ulti interruption
- Oracles: killing enemy wards, more threat towards you.
- Shurelya's Reverie: CDR, nice active
- Locket of the Iron Solari: some much needed armor, nice active

Late game:

- Aegis of the Legion: balance of stats, aura
- GA: sell Spirit visage, then buy GA to protect your oracles better and for more armor

so yea this is how i like to play Galio
please comment on the guide, however as i said before i won't be using tons of BBCode, colors, pictures, etc to make the guide more fancy, and i'm mainly making it to show how i think Galio should be played.
please comment/share your thoughts!

Sorry for Giant wall of text!