Karthus’ Ultimate R is an excellent tool, and it can allow him to impact the map from afar.
His afterlife can single-handedly change the tide of a fight, especially if the enemy continues to fight near him after he dies.
Karthu’s early game is relatively weak. This can make it hard for him to survive the laning phase, especially when he is up against a solid early game champion.
Karthus is a farm heavy champion and will need to soak up many minion waves and jungle camps to be useful throughout the game.
His Ultimate R deals basically no damage in the early game. This isn’t good for Karthus as he only wishes to use it when the enemy is super low. During this time, the enemy could have already been killed by your ally, and you wouldn’t get an assist.
Channelling your Ultimate R near an enemy champion could be very dangerous as they could interrupt the channel with CC.
0 - 15 min
Try to go for short burst trades with your Q in the lane. The goal is to ensure that the enemy can't all-in you during the laning phase. Ward around and just aim to play safely.
Once you get your first item component, you should spam your abilities more frequently in the lane. It will help you use your W combined with your Q to go for regular trades with the enemy. You still need to play safely, though.
On getting your Ultimate R, you should be able to finish off kills in other lanes. Make sure that you show up to neutral, objective fights as well since your E will be really effective in those situations.
15 - 25 min
Getting your core items will let you run down enemies and burn them to oblivion. Use your Ultimate R at regular intervals to ensure that you can help your teammates.
Fight near chokepoints to maximize your team fighting effectiveness. Sometimes, it would be wise to throw yourself into the enemy team, especially if the enemy frontline decides to all-in without any follow-up.
Another point in your Ultimate R will let you destroy the opposition due to your consistent burn damage. Use your E properly to make sure that you win clumped fights.
You will be able to blow up squishies with your Ultimate R with ease now. Even if they don't die, they will be too chunked to participate in a team fight.
You will be able to burn through the entire enemy team with proper positioning. Your Q combined with your W will be able to one-shot enemy squishies. Use this strategy during neutral, objective fights.
Remember that your W placement can make or break an entire team fight. Place it well and from the fog of war so that the enemy team doesn't anticipate it and take necessary precautions beforehand.
Karthus has great objective control due to the amplified damage dealt by his Q on single targets. It will allow him to finish objectives pretty quickly once he gets some items.
Level 6 is a significant power spike as it allows him to stack up his rune, as well as finish off enemies who have managed to escape with a sliver of health.
Once Karthus gets his first item component, he will spam his abilities frequently due to the increased mana. His damage will increase as well and will allow him to gain an overall lead in the game.
He gets a significant power spike at level 11 due to him getting access to his level two Ultimate R. The damage is increased significantly, mainly if has managed to procure some items along with it.
At level 9, his Q will be maxed out. Anyone who is caught out by Karthus will take a massive chunk of damage and will probably even die if they are singled out by Karthus.
Karthus can control a large part of the lane during the mid-game and pick off enemies with his ranged abilities. He can even slow enemies with his wall, which allows his team to collapse and initiate fights.
Karthus is really good during the late game. His abilities will hit like a truck due to his items. His Ultimate R will be pivotal to winning the game.
Once he gets 3 points in his Ultimate R, it will allow him to half-health squishy enemies easily. This means that anyone who is behind on the enemy team will suffer a lot.
At this stage of the game, Karthus would've maxed his Q and his E. His damage output in team fights will be very high.