Caro–Kann Defence

The Caro–Kann Defence is a chess opening. It begins: 
Black's idea for playing c6 is to support 2...d5. Usually, the next moves are:
Common next moves are 3. (the Modern Variation), 3. (the Classical Variation), 3. (the Exchange Variation), or 3. (the Advance Variation). 3.Nc3 is the most popular. 
The Caro–Kann is an asymmetrical defence to 1.e4. These are sometimes called 'semi-open games'. The Caro–Kann is thought to be more solid and less dynamic than the Sicilian Defence and the French Defence. Games in the Caro–Kann are often quiet and positional. It may lead to good endgames for Black, who has the better pawn structure.
The opening is named after the English player Horatio Caro and the Austrian Marcus Kann, who studied the opening in 1886.
Classical or Capablanca variation.
The most common way of handling the Caro–Kann, the Classical variation (often called the Capablanca variation) happens after the moves: 
For a long time, this was thought to be the best play for both sides in the Caro–Kann. White usually continues:
Although White's pawn on h5 looks ready to attack, it can prove to be a weakness in an endgame.
This variation is why people think the Caro-Kann is a solid defence. Black has a very good pawn structure, and can play c5 at the right time to fight for the d4 square. Black can castle queenside or kingside, or even leave his king in the centre. Black often has good chances in the because of his solid pawn structure and kingside pawn majority.
Smyslov or Modern Variation.
Another line is the Modern Variation. It happens after the moves: 
It was played by the first World Champion, Wilhelm Steinitz. Today, the variation is called the Smyslov Variation, or more commonly, the Modern variation. 
The move 4...Nd7 prepares Ngf6. If 4...Nf6 is played immediately, then White can trade knights and double Black's pawns.
The plans are similar to the Classical variation, except Black's bishop is not on the g6 square. However, this freedom comes at a cost because White is able to take up space in the center. White often plays the aggressive 5.Ng5!?, which puts pressure on the f7-square.
This variation can also lead to a quick mating trap with 5.Qe2 Ngf6?? 6.Nd6#.
4...Nf6 variations.
The variations begins:
The Bronstein–Larsen Variation is after:
Black has a worse pawn structure, and often castles queenside. However, Black does have compensation with the open g-file for the rook and active play. It is considered double-edged.
The Korchnoi Variation arises after:
Viktor Korchnoi has played 5...exf6 many times (including his first world championship match with Anatoly Karpov). This line has also been employed by Ulf Andersson. Black's 5...exf6 is thought to be sounder than 5...gxf6!?. It offers Black fast development, bu it gives White better pawn structure
Advance variation.
The Advance variation is 3.e5:
The main replies are:
3...Bf5 is most often played. Moves against it are aggressive lines such as the Bayonet Attack (4.Nc3 e6 5.g4), a popular line in the 1980s and later favoured by Latvian Grandmaster Alexei Shirov. A more natural development 4.Nf3 e6 5.Be2 c5 6.Be3, known as the Short Variation, was popularised by English Grandmaster Nigel Short and was often played in the 1990s.
3...c5 is an alternative which avoids the opening theory of 3...Bf5. It was used by Botvinnik in his 1961 match with Tal. In comparison to the French defense, Black gains the tempo normally spent on ...e6. However, White can counter this by opening the centre with 4. dxc5. This exposes the black pawn on d5.
3...e6 is playable, but when Black plays c5, he will be is a tempo behind the advance line of the French Defence (1.e4 e6 2.d5 d5 3.e5 c5).
Exchange Variation and Panov-Botvinnik Attack.
The Exchange Variation is 1.e4 c6 2.d4 d5 3.exd5 cxd5. The Panov-Botvinnik Attack begins with the move 4.c4.
This system often leads to isolated queen's pawn (IQP) positions. White gains rapid development, a grip on e5, and kingside attacking chances to make up for the long-term weakness of the isolated d4 pawn. The common continuation in this line is 4...Nf6 5.Nc3 e6 6.Nf3. Black's main alternatives are 6...Bb4 (a position which often transposes into lines of the Nimzo-Indian defence) and 6...Be7. 6...Nc6?! is not as good because of 7.c5!, and White plans on controlling the e5-square through the advance of his b-pawn to b5, or by exchanging Black's Knight on c6 after Bb5.
The "true" Exchange Variation begins with 4.Bd3 Nc6 5.c3 Nf6 6.Bf4 Bg4 7.Qb3. It was was tried by Bobby Fischer. The position is equal. Some of the strategic ideas are silimar to the Queen's Gambit Declined, Exchange Variation, (1.d4 d5 2.c4 e6 3.Nc3 Nf6 4.cxd5 exd5) with colours reversed.
Two Knights Variation.
This line is 1.e4 c6 2.Nf3 d5 3.Nc3. It was played by Bobby Fischer in his youth. White gets rapid development and has options with the d-pawn. Black's logical and probably best reply is 3...Bg4. After 4.h3 Bxf3 5.Qxf3, Black has the option of 5...Nf6 or 5...e6. 4...Bh5 is a complicated line, in which White can trap the bishop, although Black has much compensation.
The variation sets a trap: if Black plays along the lines of the Classical Variation, he gets in trouble after 3...dxe4 4.Nxe4 Bf5 (4...Nd7 is playable) 5.Ng3 Bg6?! (5...Bg4) 6.h4 h6 7.Ne5 Bh7 (7...Qd6 may be best) 8.Qh5! g6 (forced) 9.Bc4! e6 (9...gxh5?? 10.Bxf7#) 10.Qe2 with a huge advantage for White. Now 10...Qe7! is best. Instead, Lasker–Radsheer, 1908 and Alekhine-Bruce, 1938 ended quickly after, respectively, 10...Bg7?? 11.Nxf7! and 10...Nf6?? 11.Nxf7! 
Other lines.
White can play 2.c4. Then Black may play 2...d5 (see ). This can transpose to the Panov–Botvinnik line given above, with 3.exd5 cxd5 4.d4 or White can capture twice on d5. Alternatively, Black may play 2...e5.
Also, White can play 2.Nc3. Then Black may play 2...d5. If White replies 3.d4 then we get the main Capablanca line or the Two knights variation. Or Black may play 2...g6.
The Caro–Kann can also be reached through the English Opening: 1.c4 c6 2.e4 d5.
ECO codes.
The Encyclopaedia of Chess Openings has ten codes for the Caro–Kann Defence, B10 to B19.
More reading.
Also, more advanced: