Opening with Nf3 - beginner I came across the opening Nf3 wich I find very beatiful. I know that it could lead to the Réti opening. My question is: beside the Réti opening what are the most commun openings following the Nf3 and what are considered to be the weackness of this move?
1.Nf3 can transpose into almost any opening depending on your opponent and you, it is ultra-flexible.

Just to show its flexibility:

If you play 1.Nf3 and your opponent responds with 1...d5 then you can play 2.c4 to go into the Reti or 2.g3 to maintain flexibility and play the King's Indian Attack or some other pseudo-slav with Bf5/g4, all this stuff. Or you could play 2.d4 and it would transpose to a Queen's Pawn opening then from that point it would be a different story.

The same goes with 1.Nf3 Nf6 2.d4 where it transposes to a queen's pawn opening with an early Nf3.

As user3671618 said you could also go into King's Pawn openings after 1.Nf3 c5 2.e4 which would be a Sicilian. 

Also after 1.Nf3 g6 2.e4 would also transpose to a modern.

The point is that most Grandmasters use 1.Nf3 as a trans positional tool, like for example to get to the Catalan after 1.Nf3 d5 2.g3 Nf6 3.Bg2 e6 4.0-0 Be7 5.c4 and later d4 and White has avoided all the Bb4+ problems associated with employing the Catalan through its classical move order which is out of the scope of this post. Of Course Black does not have to play in such fashion and the drawback of the early fianchetto is that Black usually has the luxury of bringing his dark squared bishop out instead of blocking it in via e6. 

1.Nf3 is mainly used as an ultra-flexible trans-positional tool to avoid certain lines. For example after 1.Nf3 d5 many grandmasters play 2.d4 and so they avoid all the King's Indian, Grunfeld, Nimzo, Benoni, Benko systems as the pawn on d5 is already committed. One of the most famous practitioners of this approach was GM Alexander Wojtkiewicz, there is a famous book series written on him titled Wojo's Weapons, he played 1.Nf3 exclusively as a trans-positional tool.

1.Nf3 is just as good as 1.e4 and 1.d4, this can be best explained by the simple opening principle that it develops a Kingside piece towards the center! Former World Champion Vladimir Kramnnik is another 1.Nf3 devotee and many of the World's best players employ it in their repertoires.

The drawbacks are that you just cut out so many openings and lose many options, but this is why many 1.Nf3 players play it! They want to avoid the problematic defenses associated with 1.d4 and 1.e4. It is mainly used as a move-order trick and to maintain flexibility.

But I would recommend for a beginner not to play 1.Nf3 as many times you would have to venture into the English and complex sub-variations of other openings which I believe contain so many subtle-move orders so 1.d4 or 1.e4 are much better in improving your play since they are much easier to understand for the improving amateur and you gain a greater wider variety of positions from them which exposes you to many different themes and ideas and would contribute greater to your improvement.