It would be nice to see other situational items for Katarina in this guide. Some people build Hextech Revolver on her and that seems to work very well.

I can see why you like Rylai's Crystal Scepter for Katarina and it's also not that bad of a purchase, but I think there are just better options for playing glass cannon Katarina. Your goal is to deal as much damage as possible, while getting one survivability item that somehow helps you more than just a little health boost. 500 health may sound good in theory, but you're Katarina, a character that, even after having built Rylai's, still is very squishy. If you get caught you're likely to die anyway. The spell shield bubble on Banshee's Veil or second life on Guardian Angel help a lot more in that case.
But apart from that, I think your build is perfect and what I would use too with the exception of sometimes swapping out Void Staff for Abyssal Scepter.

As for the rest of your guide, I think you have made a few minor mistakes, but all in all it is good.

Mistakes:

• I think you should completely remove the Amplifying Tome start. I'd call it a "noob trap". With just one health potion and no more defensive stats, you're very likely to be forced out of lane very soon, which is pretty bad early in the game. You should replace it by a Cloth Armor start, which gives you quite some sustain trough 5 Health Potions and helps against physical damage characters.
• I think you should also mention Randuin's Omen (you can slow their whole team, considering you'll always be in the middle of them once every fight. And, of course, give Guardian Angel a mention too.
• Not sure if you did it on purpose, but you can swap the skill order at level 13 and 14. You can actually already have maxed out Sinister Steel at level 13, and not 14.
• Your masteries seem fine, however I'd personally prefer putting a point in Feast (the sustain really helps a lot) and Dangerous Game (this mastery seems to be made for Katarina!), and take out two points of Sorcery. It's not like 2.5% cooldown reduction makes a lot of difference.
• You say Katarina is very good at recovering from being behind because she can assassinate targets very fast, but I think that logic is not completely right.. to be able to assassinate a target very fast, she needs items, and most of the time she also has to be ahead of her enemy to get a kill fast. Not saying she's bad when behind, but recovering is certainly not one of her strong points.
• You should also discuss some alternative runes. For example, when playing against a Leblanc, it might be beneficial to run magic resist glyphs instead of ability power, or you might want to use movement speeds quintessences instead to roam better.. just a few suggestions.
• I'm not sure if it is a mistake, but the big 6 items in your item section really look a little messy. I'd change that up somehow. Also, maybe you can explain the use of the items a little more in-depth.
• Also, where's the detailed information on beating the counters you promised? :P

I think that concludes it. While there are some improvement to be made, I can see you know how to play Katarina and got a good idea of general guidelines. Maybe you could add a little more coding to spice up some parts, but for now I'm giving you an upvote because in my opinion you deserve it.

Those are better for survivability but a main key I really think is important and enjoy is that I think Katarina should keep her burst and shouldn't sacrifice burst for survivability;however, with Rylai's she can get health and a hefty amount of AP

BUT JANITSU I LOVE RYLAI'S ON HER.
Somewhat.
Ok only on Tanky Kat. Which works... Somehow.
Boots, Sunfire(yep yep yep yep yep), Zhonya's, Abyssal, Liandry's, Rylai's.
Sad part is no deathcap. Lol. Just saying it's funny to watch them be confused on why you arent dead yet.

If you want Survivability you should aim for Banshee's Veil or Guardian Angel. Rylai's Crystal Scepter really is not an item you want to buy.

I agree with Doran's Shield it was a boneheaded mistake and I forgot it xc. As for Rylai's I really enjoy it because of the slow,AP, and survivability for your channel ult.

I agree with you but lately I have seen a LOT of people taking it in games I play and in case one of you really enjoys that I tried to include it for the portion of people who think it is good.It's my first guide and I really appreciate feedback.

No Doran's Shield or Cloth Armor start mentioned

imo Juggernaut scales better and is better in the early game than Resistance

Dangerous Game is perfect on her

Rylai's Crystal Scepter isn't honestly an item you want to get

ever

Maybe i'm wrong but why did you take Amplifying Tome as Katarina early? She dosen't really have the damage from level 1 - 5 so it might be a problem. :/

Oh, I didn't really see that, lol. I bet there are even more stuff because I'm so blind sometimes >__>

Found it ;) in the masteries you took 1 lvl of Resistance which imo is not that great on Katarina. I think you mistook it for the classic Juggernaut , correct if i'm wrong tho ^^