4.e3: the quiet line is variation 5 of 6 in the Tarrasch Defence course, a advanced opening course for Black (ECO D32). It runs 22 moves and begins 1. d4 d5 2. c4 e6 3. Nc3 c5 4. e3 Nf6 …. White keeps the c1 bishop at home and plays a calm set-up. After the trades in the centre both sides have an isolated d-pawn. Black develops the bishops to d6 and e6 and puts a rook on the c-file. In the lesson every move is explained on a board and then drilled; it is free.
Move by move
1. d4 – White takes the centre.
1... d5 – Black claims an equal share.
2. c4 – The Queen's Gambit.
2... e6 – Black supports d5.
3. Nc3 – White attacks d5 again.
3... c5 – The Tarrasch Defence.
4. e3 – A quiet move. White supports d4 but shuts in the c1 bishop.
4... Nf6 – Black develops and defends d5.
5. Nf3 – White develops.
5... Nc6 – Black develops and presses on d4.
6. cxd5 – White opens the position.
6... exd5 – Black takes back with the pawn.
7. Be2 – A calm square for the bishop.
7... cxd4 – Black trades on d4 and opens the c-file.
8. exd4 – White takes back with the pawn. Now both sides have an isolated d-pawn.
8... Bd6 – The bishop takes an active square and aims at h2.
The lesson goes on for 6 more moves, each with its explanation.