Hello!
This is my first REAL build and I hope you'll enjoy it! I think this build is very good to Irelia because her spells uses both AP & AD but I can't decide what you like, right? I also think that you can run this build for Katarina but I'm not sure, haven't tried it... Hybrids is fun to play and buy for because it "always" got different things that "they want"!

Seal & Quintessence
I'm not very good to choose the Runes but I think especially the HP runes (the Seal & Quintessence) is very good to make Irela "unsquishy" and have a good shot to take firstblood.

Marks
The Marks, as you all can see, makes her spells to take more damage to the opponents and if you attack them and it's JUST so he dies, you can say that it deppended on your Marks! ;)

Glyph
This was my hardest choice... But I took the magic resist because it's good to have and it's kind of a high amount for a glyph.

NOTE!
Like I've said, I'm not the best to pick runes so if you have another idea, please tell me!

I run with a 21-9-0 to make sure that Irelia gets the DPS she deserves and so she does as much damage as she can. You could also go for a 9-21-0 to make sure that you'll survive but I'd advise to not go for utility!

Boots of Swiftness is great because of the speed and I love it but an alternative is Sorcerers shoes because of the magic penetration and that you'll get some extra speed from Trinity Force



Hextech Gunblade is just a MOST for hybrids, end of discussion. P.S Don't forget to use the active, for last hit or just to make some damage and slow the target!




Guinsoos Rageblade is also a most for hybrids even if it's not in the same range and as "high level" as Hextech but it's just great to have in the inventory.




Trinity Force is such good to everything, really, EVERYTHING. This is also a MOST.




The Bloodthirster is just good to have because of the massive damage it does when you've fed it up with fourty creeps but if you want something else I could suggest another kind of AD item as Infinity Edge



Rylai's Crystal Scepter is just so nice to Irelia because she can do her spells so often and every spell slows the target, she gets more HP and AP. If you'd like some more AD instead of AP you should go for Frozen Mallet

If you'r bad to take last hits on creeps you could spec some more in BLADESURGE earlygame and hit creeps with that spell but it will probably make you to buy some mana item to increase your mana and mana reg.

Exhaust is absolutly one of my few favourite summoner spells just because it can do so you'll get the kill, you can run away from the opponent or just help a teammate maybe? It also reduces their resistance if you've done like me in the Masterie tree!
Ignite is also just perfect! You can harass the opponent with it and take the last hit with it!

That's everything I have to say for now! I hope you'll enjoy it and maybe I'll do another build another time! Cya // Smulaan