Until 2006 the official score format was the one using 15 points. The IBF (International Badminton Federation) tried a new format using 21 points and that become the official one replacing the old one.
In order to get good at this game you should also master the basic skill.
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Having a correct grip on yout racket is the first thing you should learn. Two of the most common grips are the the forehand grip and the backhand grip. Just like the name suggest, the forehand grip is used for hitting shuttles on your forehand side of your body while the backhand grip is used for hitting shuttles on your backhand side of your body.
The second skill you should consider mastering is the serve. There are four types of serve. All of them have different characteristics, advantages and disadvantages. The high serve is the one that you probably need to master first out of four ones.
The third skill that is just as important as the others is to have a correct forehand overhead throwing motion. Try to practice this without using a shuttle.
Don`t get disapointed if you find it hard at first. Keep practicing and you will see the results of your work soon enough.
Next on your list are things like:
BADMINTON GRIP
BADMINTON FOOTWORK
BADMINTON SERVE
BADMINTON CLEARS
BADMINTON DROP SHOTS
BADMINTON SMASH
BADMINTON DRIVE
BADMINTON NET PLAY