Here is my Beyond the Sun tutorial where I teach the game as it is being played. Paid sponsorship by Rio Grande Games.

Teaching Timestamps:
Introduction - 0:00
Game overview - 0:29
Game start & action phase - 2:48
Research level 1 technology - 4:04
Production phase - 7:16
Achievement phase - 9:31
How the game ends - 11:01
Creating spaceships - 14:03
Jumping spaceships - 15:09
Controlling systems explanation - 15:44
Researching level 2,3, and 4 technologies - 18:51
Unlocking guild actions - 21:00
Colonize action - 38:58
End game scoring explanation - 42:39
Expert technology tableau variant - 45:47

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