The problem shown is a relatively simple example. It is a selfmate in two by Wolfgang Pauly from The Theory of Pawn Promotion, 1912: White moves first, and compels Black to deliver checkmate on or before Black's second move.Wolfgang Pauly, 1912
If White can leave Black with no option but to play Bxg2#, the problem is solved.
The only move by which White can force Black to deliver checkmate on or before move two is 1.c8=N. There are two variations:
Note that only a promotion to a knight works on move one: any other piece would be able to interpose after 1...Bxg2+.
A derivative of the selfmate is the reflexmate, in which White compels Black to give mate with the added condition that if either player can give mate, they must (when this condition applies only to Black, it is a semi-reflexmate). There is also the maximummer, in which Black must always make the geometrically longest move available, as measured from square-centre to square-centre; although this condition is sometimes found in other types of problems, it is most common in selfmates. Another variation is the series-selfmate, a type of seriesmover in which White makes a series of moves without reply, at the end of which Black makes one move and is compelled to give mate.