Plans in the Petroff Defense What are the typical middlegame planes for black/white in the Petroff defense, more specifically in the variations:


Petroff three knights: 1. e4 e5 2.Nf3 Nf6 3.Nc3.
Classical Variation: 1. e4 e5 2. Nf3 Nf6 3. Nxe5 d6 4.Nf3 Nxe4 5. d4 d5.

2.1. Classical Variation with 5. Nc3.
Steinitz Variation: 1. e4 e5 2.Nf3 Nf6 3.d4.
This is really really wide and there are entire books written on this topic. But a few words of comment from me:

ad 1: First of all, it's not necessarily Petrov's anymore. 3. ... - Nc6 transposes into Four Knight's / Scotch for example (yeah, entire books here as well). 3. ... - Bb4 is a bit more "Petrov's" move. Then something like 4. Ne5 - 0-0 5. Be2 - Re8 6. Nd3 - Bc3 7. dc3 - Ne4 and we have a kind of Ruy Lopez with a tempo more.

ad 2: a) I think there's no point in typing here whole lines of theory. In this variation, IMHO, you need to prepare c4 sooner or later. Otherwise it's unlikely to get advantage. The second line you mentioned 5. Nc3 is about getting ahead in development. The cost of it isn't that high. It's doubled c-pawns which are not an issue as long as there are pieces on board. (Fortunately, black has d-pawn. With e-pawn those structures might be problematic when it comes to endgames. So a tip from this sentence might be "rather don't exchange on e5 letting black capture with d-pawn"). Usually White is able to launch some attack on black's kingside castle.

ad 3: I have never played those lines in my life. Sorry.

Anyway, Petrov's defense is rather logical and quite easy to play. You don't even have to know theory very well to get slightly advantageous position by thinking at the table. As I mentioned before, you should narrow your question a bit. To get a really valuable answer we would have to rewrite whole books here :)