Quantik

From BoardGameGeek:

Quantik is a pure abstract strategy game. The goal is to be the first player to pose the fourth different forms of a line, a column or a square zone. Each turn the players will put one of their pieces on the boardgame. It's forbidden to put a shape in a line, a column or an area on which this same form has already been posed by the opponent. We can only double a shape if we have played the previous one ourself. The first player who places the fourth different form in a row, column or zone wins the game immediately, no matter who owns the other pieces of that winning move. -description from the publisher