Knight C3 pin

What is the best way to handle this pin? Move the bishop to D2 or ifthe knight gets taken, take back with pawn?

I kinda like taking it backl with a pawn and then move my bishop on A3 to block castling for my opponend but in the QG lines what is the best way of dealing with this pin?

Can you guys share your thoughts on this and explain why?

Much appriciated :)

This is called Nimzo-Indian defence. The main line is to move Qc2 with the plan of a3 and after Bxc3 Qxc3. Bd2 is possible, but i think it is better placed on g5. If you capture bishop with pawn you have doubled pawns which can be a target for black.

Actually, the best move here is debatable.  Move order is critical:

1.d4 d5 2.c4 e6 3.Nc3 Nf6 4.Nf3 Bb4 - This actually isn't the Nimzo-Indian, it's the Ragozin Variation of the Queen's Gambit Declined.  It can come from a Nimzo-Indian move order, 1.d4 Nf6 2.c4 e6 3.Nc3 Bb4 4.Nf3, but then 4...d5 is a direct transposition to the Queen's Gambit Declined while the main lines for Black are 4...b6, 4...c5, and 4...O-O.

Supposedly, 5.Bg5 is best here for White.  This is different than the Leningrad Variation of the Nimzo-Indian, 1.d4 Nf6 2.c4 e6 3.Nc3 Bb4 4.Bg5, which isn't as strong, because Black hasn't committed to d5.  Typically he will play d6 in e5 in those lines, going for a dark-square blockade, but with d5 played, this isn't possible for Black.

5.Qc2 is inferior here.  After what is known as the Classical Variation of the Nimzo-Indian Defense, 1.d4 Nf6 2.c4 e6 3.Nc3 Bb4 4.Qc2, if Black plays 4...d5, 5.Nf3 is not best as it's too committal.  White should either play 5.a3 or 5.cxd5.  The former is a heavily theoretical line that I'm not going to write a novel about here.  After 5.cxd5, if Black takes with the Queen, 5...Qxd5, known as the Romashin variation, then White should play 6.Nf3 and after 6...Qf5, trade queens and try to take advantage of the better pawns.  If instead Black takes with the pawn, the immediage 6.Bg5 is stronger, not spending time on Nf3, and in a few rare cases, this knight is actually better off on e2 than f3.

A lot depends on move order, or Qc2 and an early Nf3 before Black commits is a conflict of ideas.

For a deeper understanding, you have to study up heavily on the Nimzo-Indian Defense (ECO Codes E20-E59) and the Ragozin Queen's Gambit (D38-D39, I think, don't play this line so not quite as familar with the ECO Codes for it)