Rae1 - rook a to e1. if two rooks on the first line can move to e1. R4d4 - if two rooks on the 4th line can go to d4. Ngxh2# - the knight from g captures on h2 with checkmate.

Nd2e4 - In a rare case that there are 3 knights that can go to a single square

Pawn captures are denoted as exd5 (pawn on the line e captures a pawn on d5) even if there is only one pawn that can make a capture.