White to play and win
When I first looked at this study, I thought that the solution was pretty simple: Kg3-h4 followed by g4 is mate unless black sacrifices the bishop on g5, which leads to a lost ending. But there is (as always in studies) a strong defensive idea for black which makes the solution less obvious.
1.Kg3 Bc7+ 2.Kh3
White wants to play g4, but black can prevent it.
2...Bg3!
White cannot take the bishop because of stalemate.
But white can exploit that black has hardly any moves in this position. Note that black's only move is 3...Bxh4, since all other bishop moves would allow 4.g4#. So white knows where black's king and bishop will end up and can set up a knight fork.
3.Nb3! Bxh4 4.g4+!
Forcing the king to take on g5, placing it on a dark square and trapping the bishop on the e1-h4 diagonal.
4...Kxg5 5.Nd2
And now black will lose the bishop.
5...Bf2 (or 5...Be1 6.Nf3+) Ne4+