Hyperdrives allow travel to stars outside of the systems with jump gates. With a Hyperdrive fitted to your ship, you can select a faraway star in the Map and jump to it.
The Hyperdrive uses Hydrogen as fuel. [Class of ship] x [Distance in light years] * 1.5 = [Amount of Hydrogen required].
The Hyperdrive wears out with use. It will no longer be usable after about 100 light years of travel. Hyperdrives can be repaired at Space Stations for a fee, or for materials at your Private Space Station
If you find yourself stranded at some far away star system with no fuel or a worn out Hyperdrive, there is an emergency jump back to Ceres to save the day.
The Class 1 Hyperdrive can be purchased on SS Plato, in the Contracts Board. These are produced by NPCs and the usual price is 1,800,000 credits. You can also find Class 1 Hyperdrives on the Galactic Market, which are produced by your fellow players, and are usually sold at a substantial discount.
The Class 1 Hyperdrive can only be fitted to a Class 1 Space Ship (Turtle or Hornet - either of which is capable of completing the Susan Steele missions successfully). Class 2 Hyperdrives can only be fitted to a Class 2 Space Ship (Sparrow), and so on.
Bigger class Hyperdrives need to be manufactured at a private space station, by up-class researching the Class 1 blueprints that you get upon completion of the Susan Steele missions. Manufacturing a hyperdrive requires a Blueprint (Susan Steele will give you the Class 1 Blueprint, and you can use your Research Lab to upgrade the class if you want a hyperdrive for a larger ship). You will also need a Shipyard to construct the hyperdrive, and adequate materials in your Starbase Warehouse (Electronics, Mechanical Parts, Niobium, Tin and Carbon) before you can commence construction.
Bigger class Hyperdrives can also be purchased from your fellow players on the Galactic Market. Specify Ship Module, and search for Class 2 Hyperdrive (or whichever class you are looking for, which must correspond with the class of Space Ship that you'd like a hyperdrive for).