In order to get up to speed on the Mass Effect storyline before jumping into Mass Effect: Andromeda, here is what happens in the first Mass Effect game.
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The Story for Mass Effect: Andromeda follows a brand new character by the name of Ryder and begins right after the events of Mass Effect 2 just before the Reaper invasion. Ryder begins his/her 600 year trip to the Andromeda Galaxy in cryo-sleep and wakes up as one of the first humans ever to explore the Andromeda galaxy.
Ryder is a Pathfinder, a combat trained but untested explorer who is leading an expedition into the Helius Cluster situated in the Andromeda Galaxy. Ryder inherits his/her pathfinder status from his/her Father, the previous Pathfinder for the Tempest, a ship that is quite similar to the SSV Normandy which first made its appearance in the first Mass Effect game.
Ryder’s main mission is to establish a new home for the human race. As Ryder explores this alien galaxy she/he will come across a plethora of new challenges including savage and untamed wildlands and cut throat alien races. Ryder will also be tasked with building brand new colonies to sustain human life.