Gonu

Record vs AI

Cham-gonu is played with 12 pieces each.

Take turns placing one piece on an empty point.
Get 3 of your pieces in a row (horizontal, vertical or diagonal) and shout "Kkon!" to capture one opponent piece.
During placement, a captured point gets a stake (X) and no one can place there.
Once all 12 are placed, the stakes are removed and you move one step along the lines to make rows of 3 again.
Win when your opponent has only 2 pieces left or cannot move.

Umul-gonu is the simplest gonu.

Each side has 2 pieces and moves one step along a line to an empty point.
The bottom line with the well cannot be crossed.
On the very first move, a piece beside the well may not move to the center ("the well-gonu first move" rule).
Trap your opponent so they cannot move to win. No winner after 60 moves is a draw.

Hobak-gonu is won by trapping, not capturing.

Each side has 3 pieces starting in its home (the three end points at the top or bottom) and moves one step along the lines.
Inside the circle, pieces move freely along the lines.
A piece that leaves home can never enter its own or the opponent's home again.
Leave your opponent with no moves to win. No winner after 80 moves is a draw.

Neojul-gonu is won by sandwich captures.

On a 4x4 line board, each side starts with 4 pieces on its back row.
Move one step forward, back or sideways along the lines.
When two of your pieces and one opponent piece stand in a row, that piece is captured. (Checked only right after your move; two or more enemy pieces side by side can't be captured.)
Win when your opponent has one piece left or cannot move.

Jadongcha-gonu captures by driving around the corner wheels.

On a 4x4 line board, each side starts with 4 pieces on its back row.
Normally pieces move one step along the lines.
To capture, run along the outer lines and go around at least one corner wheel; after that you may race any distance and capture the first enemy piece you hit.
You can't pass through other pieces on the way.
Capture all enemy pieces or leave them with no moves to win.

Rule sources: Encyclopedia of Korean Culture (한국민족문화대백과사전), Ministry of Culture kids site (문화체육관광부 어린이 누리집)