So, Katarina has to be one of the most lethal and best characters when played in a solo lane or as a team fighter. Any stun or slow on your team will always give you the upper hand in a fight. Alright lets talk gameplay.

EARLY GAME:

First item I recommend is a Doran's Shield with this item let's you be a little tougher in the early stages of the game.

Then your next item would be and amplifying tome then work your way up to Morello's Evil Tome. Now lot's of people say what a waste because of the Mana Regen yes i agree the Mana regen is pretty useless but that a side the 75 AP and 20% cooldown is well taking.

Now get your self a pairs of Sorcere's Shoes for the magic penatration.

After you finish Morello's get yourself a Mejai's Soulstealer because at this point in the game your most likely to be doing lots of kills and ***its and the end of the game when you are full stackare greatly appreciated.

This is a personal choice i like this item because of the life steal and the little extra damage it give. Hextech Gunblade is a nice hybrid item witch allows you to have a bit of everything... LS, AD and some AP. 20% isn't much but it can help you survive. You finish killing and enemy your low on health find a minion and regen a little.

Now this item is a essential part of the build. A Rylai's Crystal Scepter the 500 health and the 80 AP is very nice to have but the most important part of this item is the 35% slow for 1.5 sec. This item will allow you to make sure your enemy those not escape, except if his using flash.

Last but not least Rabadon Death Cap with its 155 AP and its 30% AP boost this will maximize your damage to it full potentail.