Unfamiliar with this move notation I'm not even sure what to call this one. I'm reading Caro-Kann Defense: Advance Variation and Gambit System by Anatoly Karpov.

In the first chapter karpov mentions a move order:


e4 c6
d4 d5
f3


So far so good - the gambit system. Then he mentions black has a few continuations. The one that I'm not sure how to put on my board is:


...de 
fe e5 


I've never seen the notations de and fe used before. I thought they were for captures but it's very clear karpov is using normal capture notation (with 'x') throughout the book.

How do I understand this notation?
de and fe are normal pawn captures. There is no contradiction in writing de and NxB and Nxe5. The "x" is optional.

It would be unusual and inconsistent to write 4. BxNc6 and 4. ... Nc6 in the following -
1. e4 e5 2. Nf3 Nc6 3. Bb5 Nge7 4. BxNc6 Nc6

but if we put it in fen then it works -

[FEN ""]    
1. e4 e5 2. Nf3 Nc6 3. Bb5 Nge7 4. BxNc6 Nc6


Note what the latest FIDE Laws of Chess say about this -


  C.9 When a piece makes a capture, an x may be inserted between:
  
  C.9.1 the abbreviation of the name of the piece in question and
  
  C.9.2 the square of arrival. Examples: Bxe5, Nxf3, Rxd1, see also
  C.10.
  
  C.9.3 When a pawn makes a capture, the file of departure must be
  indicated, then an x may be inserted, then the square of arrival.
  Examples: dxe5, gxf3, axb5. In the case of an ‘en passant’ capture,
  ‘e.p.’ may be appended to the notation. Example: exd6 e.p.


(Italics added for emphasis)