Copyright (c) 2003 SuperDimension Games

This game is played on the following board with the following setup:

STACK - A stack consists of up to eight stones of either color.
The player that owns the top stone, owns the stack.
Each stone at the setup is a stack of size 1.
BOARD - Each board cell is connected to:
any orthogonally adjacent cell at the same 4x4 square; and
the analogous cells at orthogonally adjacent 4x4 squares.
TURN - On each turn, each player must move a friendly stack. 
The player takes, from that stack, up to 4 stones, always removing from the top and without rearranging. Then, he moves those stones to the top of any adjacent cell (which may be occupied by a friendly or enemy stack). 
This movement can continue to another adjacent cell (it is possible to return to the original cell), but for each step, the player must leave at least one stone (taking them from the bottom).
GOAL - Wins the player that captures all enemy stacks.

Since a player can only move stacks up to 4 stones, a multiple movement can only have 4 steps. Because of this board topology (a tesseract projection), there are numerous ways to execute a sequence of 4 steps with a single stack.

A moving sample

The white stack can move from [1] to [4], dropping one white stone of each cell and leaving 2 stones behind.

If White makes that move, the remaining stack will turn black, since a black stone will be on top. 

A sample endgame 

White's turn. 

He can win the game by moving his stack of size 4 into the marked cells.

Check the official website for Tessaron with lots of information.