As Black
The Caro-Kann
The solid answer to 1.e4: a good bishop, a sound structure, and no memorised disasters. Covers the Advance, the Exchange, the Panov and the Two Knights.
The Caro-Kann answers 1.e4 with 1...c6, preparing 2...d5 with a pawn instead of a piece.
The one idea worth keeping. In the French, 1...e6 locks the light-squared bishop in for the whole game. The Caro-Kann plays 1...c6 first precisely so that bishop can come out to f5 or g4 before ...e6 shuts the door. Almost every Caro-Kann mistake is a version of forgetting to get that bishop out first.
Why it suits an improving player. The structures repeat, the piece placement is nearly always the same, and there is no line where a single forgotten move loses on move eight. You will lose games in the Caro-Kann, but you will not lose them in the opening.
What the course covers
The Classical
3.Nc3 dxe4: the main line, and the bishop's route out.
Classical main line
1.e4 c6 2.d4 d5 3.Nc3 dxe4 4.Nxe4 Bf5 5.Ng3 Bg6 6.h4 h6 7.Nf3 Nd7
The Advance
3.e5 grabs space. You undermine it.
Advance, 3...Bf5
1.e4 c6 2.d4 d5 3.e5 Bf5 4.Nf3 e6 5.Be2 c5 6.Be3 Nd7
Exchange and Panov
3.exd5 leads to two very different games.
The Exchange
1.e4 c6 2.d4 d5 3.exd5 cxd5 4.Bd3 Nc6 5.c3 Nf6 6.Bf4 Bg4
The Panov Attack
1.e4 c6 2.d4 d5 3.exd5 cxd5 4.c4 Nf6 5.Nc3 e6 6.Nf3 Bb4
The sidelines you will actually face
Two Knights and the Fantasy, both common under 1800.
The Two Knights
1.e4 c6 2.Nc3 d5 3.Nf3 Bg4 4.h3 Bxf3 5.Qxf3 e6
The Fantasy Variation
1.e4 c6 2.d4 d5 3.f3 e6 4.Nc3 Bb4 5.Bf4 Ne7