Building the Hyperdrive

Upon leaving your "home" planet, you should receive a beacon signal alongside a new set of objectives to build a fully functional hyperdrive for your ship. This is a key piece of technology that opens up the universe by allowing you to travel to new solar systems. That said, track the beacon signal to a planet's trading outpost and speak to the alien there who will give you the Hyperdrive Blueprint.

Now to craft the hyperdrive you need a Dynamic Resonator and 200 units of Heridium. The former is available for purchase at galactic trade terminals in space stations for the price of over 26,000 credits. You can get the required amount by uploading Discoveries to the server or by selling minerals you've collected. The type of valuable minerals you have on hand will vary depending on which part of the galaxy you started in.

But personally, I ended on a solar system with an abundant supply of valuable silicates so I just mined and sold those. Otherwise you can just fly out to space and destroy debris to farm Thamium9 then sell them. As for the Heridium, hopefully you can mine some from the planet that the beacon signal leads you to. If not, then there should be some left on your "home" planet so go back there to gather what you need.

Once the hyperdrive is built, you will need a Warp Cell to fuel it. The recipe you have on hand says that 100 units of Thamium9 and one Antimatter is required to make a Warp Cell. The Thamium9 is a common material you can mine from destroying debris in space. As for the Antimatter, track the new beacon signal to another outpost where an alien will hand you the Antimatter. Use these materials to make a warp cell which gives you ship just enough juice to make it to a new solar system. Also, make sure you do not purchase a new ship until you get the blueprint for the Antimatter in the next star system. You will need it to be able to craft additional warp cells.