The Abandoned Mine is a mine rich in Psynergy Stone minerals northeast of the Goma Plateau beyond the Tanglewood. It and the two aforementioned locations comprise the first 3-part introductory dungeon to Golden Sun: Dark Dawn, of which this is the last part. It contains the first boss battle in the game, the Tangle Bloom.
Matthew, Karis, Isaac, and Garet must travel to and through the Abandoned Mine in search of Tyrell, who had crashed here while flying the soarwing. They find him unconscious, his energy having been sucked out by a Psynergy Vortex that has appeared here for the first time Isaac can recall, and before they can reach him they are attacked by an enormous plant monster, the Tangle Bloom. They dispatch it fairly easily with Isaac and Garet's experienced help and save Tyrell.
Once you have gone into the mine's entranceway at the end of the Tanglewood, the first small screen you come across has a Psynergy Stone to replenish party PP with. In the next, larger area, go right until you get to a plant that you cast Growth on to turn into a climbable ladder. Past that, follow the winding, linear path east and then west until you get to a large mine shaft entryway. A non-glowing Psynergy stone here will shatter when interacted with, and will not restore your Psynergy Points again.
At the large room past the entryway, another cutscene transpires that showcases the layout of the room. When you regain control, follow the linear path around until you are south of a grow-able plant and the glowing red root that blocks your way off. Your Growth Psynergy has a long enough range to turn the plant into an ivy ladder from the distance. Proceed to the top of the ivy ladder, climb down it, and hop right to where both the Psynergy Vortex and a giant flower are. Casting Fireball on the vortex will do nothing, but casting Fireball on the plant will trigger the game's first boss battle, the Tangle Bloom. The fight cannot be lost because of the involvement of the computer-controlled Isaac and Garet in your party, so unleash your offensive Djinn and perform summons afterwards to win quickly.
After the boss battle, go to Tyrell to trigger a cutscene. After this, all you need to do is follow the linear series of stairs and rooms past Tyrell to the external balcony of the mine's mountain for one last brief cutscene before the story shifts back to the Lookout Cabin.