Can someone explain Death Note to me please?

Okay this kid named light gets a "death note" a note book that belong to a shinigami-death gods (kinda like grim reapers) If he writes a persons name in it they die. So to create a "pure and better society" Light starts killing criminals and other bad people in hopes of someday ruling a perfect world. The government starts to take notice when all of there criminals start to die in jail so they assign top-secret FBI agent 엘 to the case. So throughout the series Light (kira) and 엘 (ryuzaki) fight each other. Light can't kill 엘 unless he knows his real name, 엘 can't catch Kira unless he knows who he is. (by the way both of them are some of the smartest people on the planet) There's manga, anime, and 영화 on the series. That's would pretty much be a basic over view of the series. Hope this helps some.

Heres the discription on the back of the Dvd for you:

Light Yagami is an ace student with great prospects - and he's bored out of his mind. But all that changes when he finds the Death Note. A notebook dropped 의해 the rogue Shinigami death god. Any human whose name is written in the notebook, dies, and now Light has vowed to use the power of the Death Note to rid the world of evil. But, when criminals begin dropping dead, the authorities send the legendary detective 엘 to track down the killer. With 엘 hot on his heels, will Light lose sight of his noble goal... 또는 his life?