Beowulf is played in three acts.  Each one has a different board.  The first one is a simple square grid.  The second is the same size, but has some obstacles on the grid as blockers.  The third is twice the size, but oriented on the diagonal.

During the game players draw and place tiles on the board, or they can place one of their figures on a spot instead.  For every one of your figures on the board, you will gain points based on the value of the tiles in that row and column.  

If you place a tile with a high point value, then your opponent(s) will want to place their figurines in that same row or column.  

Your strategy also has to take into account the value of each figurine.  They have multipliers of 1 through four.  The four 1x ships can be used in every act.  There are only three 2x, two 3x and one 4x figure.  If you use a 2x-4x figure, it cannot be recycled on the next act, so you have to decide whether to use them on a good point location, or save them for later.

Not all of the tiles are positive in value.  There are a smaller number of negative tiles that effectively act as attacks.  You want to place those on columns and rows with higher value enemy figurines.  

There are also special tiles that allow you to swap figures, slide a figure to a new row or column, destroy and replace a similar special tile, make everything in a row or column negative, and increase the rank of everything in that row or column.

At the end of each act, players add their points and gain victory tokens that carry to the end of the game.