• The game starts on an empty board. Players move in turn to place one stone on an empty cell. White moves first. The second player is entitled to a swap.
• The game is won by the first player to complete a ring or a bridge or a fork. All of these are 'chains': closed connections of one color.
  
  
  • A ring is a chain around at least one cell
  • A bridge is a chain linking two corners
  • A fork is a chain linking three sides. Corners do not belong to either side

That's it. In 'New Rules for Classic Games', Wayne Schmittberger states that a ring should surround at least one vacant cell.
This is not the case: the cell may be occupied by either player.