Hope To hear positive feedback on my very first build :)

+1'd Brotato. Good guide, only thing I'd suggest is getting the Tear of the Goddess BEFORE the Catalyst The Protector to maxamize your mana gain.
Also, the 21-0-9 masteries puzzle me.
Wouldn't it be more effective to have the full EXP mastery, the mobility from the Movement Speed mastery, along with the 15% Reduced Cooldown time from the Presence of the Master in the Utility Tree?

@ Incendiax

Thanks, And ya I agree I probably should fix that.
Also the 9/0/21 Masteries, as i said are depending on personal tastes. If you need the extra mobility from it then go for it. Also The 15 percent reduced cooldown time isn't exactly necessary unless you depend on your summoner spells. I rarely flash/Teleport so I never really use em. I Like the 21/0/9 Because Its all about dishing out the most damage with the increased Damage from the Offensive tree. It makes your req hit harder, Q hit harder, Etc. And with the Brute force making ur attacks deal more damage and the extra damage to minions, It gives you a stronger pushing advantage than the 9/0/21 Approach. as I said its all about personal Tastes.

+1 nice build and guide but you should think of adding color to your guide

@ VKZ95 Yah thats true lol. Im a noob to writing guides so i forgot u can do that. Alright, I'll spruce it up now

im glad too see colors on your guide but you should use green instead of red when talking about something good ( pros, spells that work) I think you can learn alot from this guide jhoijhoi it helped me making my first guide

Will do i'll check it out thx

Well... few glaring problems here.
Your item build is good but, you should probably get either Archangels earlier or Rylai's later. Just my preference, you should not be getting that much mana so early on through the Tear and Catalyst. Try throwing AP in the mix earlier.

Your skilling very awkward. Try focusing one one simple path.

Also, your masteries are really weird... Good Hands > Perseverence Especially on Karthus. Ususal caster masteries are 9/0/21. You don't need anything in the offence tree other than the magic pen , the CDR and the small AP boost. Brute force only improves damage from your auto-attacks... That's not that great of a bonus to Karthus. The mana bonus from Expanded Mind is so small that, end-game, you get an extra 51 mana because it works off your base mana. Also, not having those points in Awareness will put you behind in levels if the other mid laner does.

Seals are really your preference but, until you get some more mana regen from killing minions with Defile off, you're not going to have a lot of mana. I would suggest getting either flat MP5 or MP5/level seals.

Other than those things, this is a very solid guide. It explains things well and gives reasons for everything. I have not voted but, I hope this will help you inporve overall.

@ Lugignaf

I totally agree with your decision on good hands greater than perseverance. I made this mastery tree back when he didn't get the extra 20 percent less time dead on his passive. But since he doesn't It's probably best since hes a good dive bomb char. agreed.
yes I read up on the expanded mind and It really doesn't give you that much really. With Tear's i'm usually better off, the extra points in the EXP are great, I will change, thank you.
However As i said the 9/0/21 is something I can't agree with. Your right brute force only works for attack damage, I know... but It's extremely good for pushing, since that relies on you attack damage (damage to towers), Since it''s essential. However The critical strike bonus is the only bad thing in the offensive tree for karth, But the Increased 4% Damage from Havoc is so much better than presence of the Master IMO. But as I said its all up to personal Taste.
When you say that im not gonna have a lot of mana, your correct. But, I don't spam my Q like all other Karthuses do. I correctly time it and I make sure I have enough mana til I get tears, then I just go all out, lol. But since not everyone can be mana conservant, I will add those runes as a alternative route in the guide, Since what you said is true and I should of pointed that out, thanks for the comment :)

Np.
Towers aren't based on your AD completely. It takes whatever is higher from 40% of your AP or your total bonus AD.
Karthus us a natural pusher wit his AoE and spammable skills so, the extra 3 AD isn't really worth it. It helps get last hits early on with his terrible attack animation but that's it.

I can speak from experience playing with Avion (Im one of his usually team mates) that this build is quite effective. People usually rage agenst him after he reaches about 20 kills and 2 MAYBE deaths. Its an effective build for sure.

Very comprehensive. Nice job.