There's only one path you can go for now, so jump onto the little islands and double jump up the ledges. As you continue, there will be some kind of quake that will cause a canyon to appear, so hover over it. There will be another big canyon that appears, so glide down and go through the nearby tunnel, gathering the Raritanium. Keep going until you spot some Thugs bothering someone. Take them out and there will be a short scene, where you will get the Grav Tether.
To work this gadget, you need to aim at the purple targets on the walls, using L1 and then pressing Circle to fire. The first shot determines the direction, so you need to think about which way your going. When they're connected, a beam appears that you can jump into to ride to the next area. When you want to destroy a beam, aim the Grav Tether at one of the targets and "fire" at it.
Use the Grav Tether to cross the first gap, then destroy the beam and use it to cross the next gap. Go forward and clear the area of Thugs, and you'll find a weapons vendor here. There are two new weapons you can buy, the Nightmare Box and Temporal Repulsor, as well as upgrade your already-acquired weapons with Raritanium (there's some behind the kiosk). Once you're finished, you have two objectives now on your map, to investigate the Thugs-4-Less Outpost and to enter the Azeril Caverns.
