As a militaristic state, it would perhaps come as no surprise that the primary responsibilities of Noxian women are raising strong children and providing succor for husbands who walk the path of soldiery. There are some, however, for whom nurture is not nature, and Katarina is just such a creature. Born the daughter of the feared Noxian General Du Couteau, the girl was always more interested in her father's knives than in the dresses, jewelry, and other trifles that her sisters spent so much time fussing over. A childhood dispute soon unveiled her uncanny knack for bloodshed, and her father, ever the opportunist, happily fostered her killer instincts. After training under the tutelage of the finest assassins the mighty city-state had to offer, Katarina first cut her teeth performing assassinations in the Ionian War. There, her ruthless mastery of the knife and dagger combined with her sadistic temperament to earn her the title Sinister Blade, a moniker that would follow her for the remainder of her career. She is most famous, however, for her exploits in the campaigns against Demacia, especially those surrounding her engagements with the nation's champion, Garen; a rivalry which began when she recovered the remains of Sion from a vanguard under his protection.
With the demand for warfare somewhat arrested by the tenuous peace settling over Valoran, Katarina sought the allure of violence in its last remaining haven: The League of Legends. Some might say it was an inevitability that Katarina's chosen path would draw her to become a champion of the League, continuing to enforce the will of Noxus and bring prestige of war to her noble family. There, she continues to perform her bloody work - esteemed and reviled, feared and adored.
"The Sinister Blade of Noxus is like a black widow - beautiful, but deadly."
Garen, the Might of Demacia, following a skirmish in the field

This build is a tanky hybrid Katarina leaning a little towards Ad. This build allows Kat to absorb a lot of damage and deal out a whack as well. I am not going to lie you will do more damage with your ultimate if you went strait ap but if you use this build you will be able to survive the entire team fight not just while spinning which will allow you to do more damage overall this build also caps at about 230 ad so you can still deal good damage while auto attacking.

You may look at the runes I use and say what the **** well yes they do look rather weird but they serve a very good purpose by using ap per blues and ad per yellows and quints you can make up for what would be a weak late game due to the high item price of warmogs. The ad per lvl are cheap as well 205 each (if you can't afford the ap per blues you could use flat ap if you already have them or ad per lvl.)

if I get positive feedback about the core build I will add more to this guide (like how to use abilities item choice in detail ect.) So rate and comment please !