Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
This is 1 way of playing Karthus and doing huuuge amount of damage.
The item sequence is not a must after the 1st Staff, that is a must to build up mana for the 3% AP bonus on it.
The last item is just a random... you can take some more penetration (Void Staff, Abyssal Scepter)if you fight vs. magic resist tanks like Galio.
Summoner spells can be changed but don't take useless ones for this champion. You should only choose between flash, ghost, teleport,ignite maybe but that's about it! Don't use clarity or heal or any of that, you don't need it.
Rate and leave a comment if you want, and remember to try new things!