Metroid Prime happens after Metroid but before Metroid II.  Metroid Prime has a uniquely new story.  Since the game doesn't really give off a story, I will explain it in my own words.
After Samus Aran destroyed the space pirate leader, Mother Brain, and escaped Zebes, Samus received a unendentified distress beacon from an unknown ship orbiting Tallon IV.  Samus entered the ship and discovered a mess of dead space pirates and and lurking in the shadows, parasites.  After she destroed the the Prasite Queen, she discovered Meta Ridley.  The Meta Ridley escaped and Samus nearly escaped while gaining many malfunctions.  She headed toward Tallon IV and went through all the dangers on Tallon IV.  She discovered horrible expirements, strange new creatures, and the secrets of Phazon.  What else is there?
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