kings Indian attack

Research it on wikipedia

Yep. It is the most favorite opening Fischer used when he was still young(tournaments) and his chess career is stil fresh. 

You can study it(the Kings Indian Attack) but it would be very tedious and needs a lot of time and patience. Bobby Fischer also uses Ruy Lopez most of the time against any black opening and he chooses close positions against black. =) Hope I helped.

"... For players with very limited experience, I recommend using openings in which the play can be clarified at an early stage, often with a degree of simplification. To accomplish this safely will take a little study, because you will have to get used to playing wiith open lines for both sides' pieces, but you can't eliminate risk entirely in the opening anyway. ... teachers all over the world suggest that inexperienced players begin with 1 e4. ... You will undoubtedly see the reply 1 ... e5 most often when playing at or near a beginner's level, ... After 2 Nf3, 2 ... Nc6 will occur in the bulk of your games. ... I recommend taking up the classical and instructive move 3 Bc4 at an early stage. Then, against 3 ... Bc5, it's thematic to try to establish the ideal centre by 4 c3 and 5 d4; after that, things can get complicated enough that you need to take a look at some theory and learn the basics; ... Of course, you can also play 1 d4 ... A solid and more-or-less universal set-up is 2 Nf3 and 3 Bf4, followed in most cases by 4 e3, 5 Be2 and 6 0-0. I'd rather see my students fight their way through open positions instead; however, if you're not getting out of the opening alive after 1 e4, this method of playing 1 d4 deserves consideration. ... a commonly suggested 'easy' repertoire for White with 1 Nf3 and the King's indian Attack ... doesn't lead to an open game or one with a clear plan for White. Furthermore, it encourages mechanical play. Similarly, teachers sometimes recommend the Colle System ..., which can also be played too automatically, and usually doesn't lead to an open position. For true beginners, the King's Indian Attack and Colle System have the benefit of offering a safe position that nearly guarantees passage to some kind of playable middlegame; they may be a reasonable alternative if other openings are too intimidating. But having gained even a small amount of experience, you really should switch to more open and less automatic play." - IM John Watson in a section of his 2010 book, Mastering the Chess Openings, Volume 4

For more on KIA, one can also try The King's Indian Attack by GM Neil McDonald.

"The King's Indian Attack (or KIA) is a flexible opening system that can be employed by White after 1 Nf3 or against the French, Sicilian, and Caro-Kann if he chooses to begin with 1 e4. ... If you play 1 e4 you aren't guaranteed to get a KIA opening system: for example, after 1 e4 d5 there's no good way to maintain a pawn on e4. ... [For 1 Nf3] a possible drawback compared to 1 e4 is that you have to face the solid Slav line after 1 Nf3 d5 2 g3 c6 in which Black puts his bishop on f5 or g4 in the near future. Facing the Dutch after 1 Nf3 f5 might also not appeal to some players." - GM Neil McDonald (2014)

My humble opinion is Yermo is right when he says black and white should have a different approach on openings.

As Dvoretsky mentioned in his book "Opening Preparation", most chess players don't just scratch their head and say "How about studying, er, the Nimzo-Indian?"

The point is, to just blindly ask some blanket statement about playing a certain opening against everything is not going to work.  As pfren already said, you can't just assume the same game every time.  One must truly understand the Nuances and there are many cases where the KIA is unplayable (after 1.e4 d5) or simply not good at all (after 1.e4 e5).

Fischer did not play the KIA against everything.  There is a reason for that.  He didn't play the KIA just to play the KIA.  He played it because of specific commitments that Black made in his opening moves.

Think about it this way.  Playing a "reverse" opening almost never works.  What good is the extra tempo going to do you?  Not much!  Why?  In many cases, Black's defenses are reactionary.  They rely on commitment by White.  For example, the Dutch is better than Bird's Opening because White has weakened e4 via his 1.d4 push whereas in the Bird, Black has not weakened e5.  So what does that extra tempo do?  Usually it will take the slight disadvantage of the defense and make it more of an equal position.

Take a look at the King's Indian Defense.  What moves does White typically make, regardless of variation (Classical, Fianchetto, Saemisch)?  d4, c4, Nc3, e4 (even in the fianchetto, e4 gets played around moves 8 to 10), some form of development of the Kingside pieces, and castles kingside.

Now let's flip it.  White gets nothing after say, 1.Nf3 Nf6 2.g3 g6 3.Bg2 Bg7 4.d3 d5 5.O-O O-O 6.Nbd2 c5 7.Re1 Nc6 8.e4.  No advantage.  Black will eventually get in e7-e5 in 1 go.

Now let's look at what Fischer did, and other cases where it's legitimate!

After 1.e4 e6 2.d3 or 1.e4 c5 2.Nf3 e6 3.d3, you will notice that White is headed for the same thing.  He will play Nbd2, g3, Bg2, O-O, Re1, etc.  But look at what's different!

In the Normal King's Indian, White almost NEVER plays the move e3.  Almost always he goes to e4 instead.  Black has committed in both of those lines to the move ...e6 instead of ...e5.  So now you don't have a reversed King's Indian, you have a true King's Indian Attack, which is a different opening than the "Reversed King's Indian".  Just because White's first 7 moves match that of Black's first 7 in the King's Indian Defense doesn't mean you have the same position reversed.  Black's setup is inferior to what White's setup would be in the King's Indian Defense.  Not inferior to the point of refuted, but enough to where Black is actually on the defensive as he is, in essence, a tempo down WITH an inferior pawn structure compared to what White gets in the King's Indian Defense.

So in addition to the nuances of various positions as indicated by pfren, you also need to understand when something like that can still achieve an advantage and when it's nothing more than smoke in mirrors and what will be fortunate just to hold the position.

Well said but you are not Fischer and some theoretically equal positions are better for one side and worse for the other, where there's smoke there's fire. Fischer won over time many games that were theoretically equal. It has nothing to do with unbalances either, some initially dull positions can give birth to unbalances in later stages of the game, and while it might be easier to cope with unbalances with reduced material on both sides at higher levels, it is not always the case at lower levels, and when I'm saying here lower levels, I'm thinking of levels in the 2200-2500 range.

Would it make sense to go for the Glek system?

Fischer was playing the KIA only when Black was committed to a French type pawn structure with e6-d5 or the Sicilian order c5-e6. The idea of this was to take advantage over the light squares (g4) on the King side since Blacks light square Bishop is locked inside the pawn structure and use the extra minor piece ( knight) to exploit imbalances.

From Fischer's period theory has changed a lot. It's not easy for White to seek an advantage in those positions and definitely not in modern correnspondence era.

What I suggest to the OP or any beginner is to study the KIA as a game positionally and understand the tactics getting involved. It's good games and positions to train someone but not to play for a winning result. There are better options.