French Defence: Black gets a cramped yet solid position with the idea to get counterplay on the queenside or undermine white's center before white crushes him on the kingside. Black dreams of trading off his lame light squared bishop, white would love to avoid this and press his spacial edge.
Summary of openings
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Queen's gambit: White puts pressure on d5, threatening to capture and take the center. Black often defends his center with ...e6 or ...c6, but can also dismantle it with ...dxc4 and use the time that white uses to regain it to consolidate his solid position, intending an eventual ...c5, when white can either simplify with sterile equality or plan to recapture on d4 with exd4, with an isolated pawn in exchange for piece activity and space. In the QGD, white usually pins the f6 knight and because of his space and pins he has the more comfortable, active position, and also can open the c file whenever he wants. It also makes black second guess playing ...e5 or ...c5, since that could loosen his structure after pawn exchanges, often giving him an isolated pawn. So black wants to free the cramp with exchanges and pawn breaks, a common one being ...dxc4 followed by either a pawn break or a knight move, trying to exchange bishops. White's ideas include opening the c file with cxd5 if and when the time is right, playing e4 favorably, and building up his position with moves like Qc2, Bd3, Rc1 etc, because black won't be able to do the same if he doesn't take action in the center. White always needs to keep in mind black's freeing maneouvers, and how to react to them.
The slav is a little complex and has many different branches, so I'll stop here for now.
I thought it might be interesting to summarise common chess openings. This would be a very useful tool for new studiers of opening theories to gain an understanding without having to go into great detail with every opening.
A really good summary might include general aims of both sides for the game and what sort of game usually results.
Caro Kann:
Black aims to gain some control of the centre without creating any weaknesses. Also aims to set up a solid pawn strucutre that will be favourable in the end game. Black often tries to exchange of its weak white squared bishop.
If white castles queen side then an attack by black is possible by targetting weak pawns.
White aims to gain space and a lead in development by activating its minor peices. It may look for a kingside attack by exploiting the light squares.
Often leads to a positional game.