Okay guys, here's my build for Katarina. It involves a lot of AP, and since non of here abilities use any sort of resource you can keep casting and casting.

For runes I like a good balance in cooldown reductions and boosted ability power. The faster you can get her abilities back, the more damage you can throw out at the enemy.

Pretty basic master build for high AP.

For items I always start with the minor boots for some extra speed in getaways. After that, Rylai's Crystal Scepter can get incredibly helpful, as it makes your spells slow the target. Which in a chase makes it very rewarding. The extra health and Ability power don't hurt either. Building the Hextech Revolver is another big help by adding spell vamp, making trips back to the shop less frequent. These items give you a good base, so a Kage's Lucky Pick is a good next item to help get some of the bigger items like Rabadon's Deathcap. But if you haven't already, picking up some Sorcerer's Shoes will help speed you up some more, and allow more damage to get through to the enemy with the magic penetration it adds. After buying a Rabadon's, a Will of The Ancients is a good idea, as it builds off the HexTech Revolver and grants you and your team mates some more Ability Power and Spell Vamp. Next up is the Abyssal Scepter, another team helper. This item lowers the magic resist of nearby enemy champions, while also raising your own. Finally, selling Kage's Lucky Pick will give you the space for a Void Staff, giving you that last bit of Ability Power, and a ton of Magic Penetration. Now if you do decide to stray from this build, remember that Katarina Does Not Use Mana. Stay away from items that give Mana and Mana regeneration.

For Katarina's Skill Sequence, you might want to vary depending on what sort of situations you get in. I would always get her Q first though, as it lets you poke an enemy without having to commit to a full fight. Her Q also bounces between minions and champions, marking them so getting W at lvl 2 can help consume that mark and deal a lot of damage to all enemies around her. Another bonus to her W is that when it hits an enemy champion, it gives her a movement speed boost that can help in a chase as well as an escape. Katarina's E is good for chasing enemies, starting fights, and for escapes. It's a teleport that is used by targeting an Enemy or an Ally that gives you a short shield right afterwards. So in combination, hitting an enemy champion with her Q to deals some initial damage and marking them, then E to teleport dealing damage and consuming the mark to deal even more damage, followed by an E to get in more damage and start chasing if needed. Katarina'a W has a very low cool down, making it even more useful. Now if you add in her Ultimate, you need to stay stationary but your damage output is humongous for a short time. It can also target up to Three champions, making it very useful in team fights. Katarina's R also has a very short cool down, at less than a minute it's one of the fastest I've seen.

For Summoner Spells, I choose flash for when a quick getaway is needed, or to catch up to an enemy champion to get in that last bit of damage for the kill. Ignite is especially helpful in the beginning to kill champions at low health that start running toward a tower.

When taking out Creep Waves, Katarina's Q will bounce hitting most of them. A quick W at a high level will wipe them out in no time at all.

Overall, Katarina is an awesome Champ to play. She has great versatility in both creep control and Champion Takedowns. And with her great mobility, Getting in and out of combat is a breeze. Mana is never an issue, making playing her even easier and very fun to play. I would recommend her to everyone from novices to experts. 3150 IP may take a bit to get to for less experience players but it is definitely worth it.