Want to carry around Blaise Muller's award-winning game in your shirt pocket? No problem: Just print the graphic below on an A4-sized sheet of cardboard, protect it on both sides with adhesive plastic (this is optional but highly recommended) and cut out the board and pieces:

Here's a brief reminder of the rules:

Players: 2
Duration: 5 minutes

The board is placed between the two players (now here's a surprise!), and all the pieces next to it in a common pool.
The starting player chooses any piece and hands it to his opponent.
From now on, the players take turns in performing two successive actions:
a) placing the piece recieved from their opponent on any free square, and
b) picking their opponent's next piece.
Pieces on the board stay put until the end of the game. The game ends as soon as either player by placing his piece completes a line (horizontal, vertical or diagonal) of four pieces with a common feature (outer shape, outer colour, inner shape, inner colour). This player is the winner. If the board is filled without a winning line, it's a draw.

Pro-Rule (obligatory once you're past the stage of absolute beginner, in order to avoid frequent draws):
Forming a square of four adjacent pieces (e.g. on coordinates A1 / B1 / A2 / B2) also counts as a win.

If you want to risk a brain-meltdown, try the following:
Any square formed by means of non-adjacent pieces (e.g. A1 / C1 / A3 / C3) also wins!

And if you're keen to make it really competitive, use a chess-clock (preferably a digital model with Fischer-mode) and set it to something like 15 seconds per move - that'll get the old adrenaline flowing!.

By the way: If you haven't got the "official" Quarto set with beautifully crafted wooden pieces, you should certainly get yourself a copy: