First I have to tell you about the sum spells, if you feel like you need flash early, go for it, but if you feel like the ult is enough you can go for exhaust if they have hard assassins like Talon or Zed, or Ignite if you want that little bit extra damage to kill them off.

Now to why is this good?
You can get insanely good ganks with your R at level 6 since you can jump over walls then just continue to follow them in lane with it since it only has a 6 sec cooldown(without CDR), you also have your burst with W and E.
And Kassadin is just generally great against squishy teams so try and pick him when you see that the enemy team doesn't have enough tanks or tankyness.

The most efficient way I've tried is Krugs -> Raptors -> Red Buff -> Scuttler -> Gromp -> Blue Buff -> Wolfs.
You need to get some HP back from Scuttler with your Machete so you can take on Blue Buff, you will probably die if you don't.
And you start Krugs since you can Auto attack cancel with your W (Auto attack then right after press W) and get 2 hits in easily, your W costs 0 mana so you don't need the extra mana regen.
After you've done your route you should go recall and buy your Tear of Goddess and Hunter's Potion, you should have pretty much exactly enough money.

This build is heavily dependent on your mana, that's why you go for a lot of mana items so you can stack up your R in team fights to get that extra bonus damage.
Always remember to activate your Murmana in teamfights since it buffs your W, Q and auto attacks.

Always use your R when it's at 50 mana (first cast) and if you have the mana for it, the second cast too (100 mana) but after that it might not be worth using it since it starts draining 200 -> 400 -> 800 mana, so your mana pool will be depleted in seconds.
Other than that your W will stack it for no cost during your whole game.
You don't really want to upgrade your Tear to Manamune until you have 750 stacks since it doesn't do much for you until it's a Murmana.