Hyperdrive is the second level of Hyperspace technology.
Hyperdrive works in an almost identical principal to the basic Hyperspace technology - it collapses space directly in front of the ship so that it has less space to travel through. Hyperdrive travels three times as fast as Basic Hyperspace, because it condenses space much more effectively by actually merging it into itself. Although it is much faster, it created many problems as sometimes space would become trapped inside itself, causing a Spacial Implosion. In response to this, the technology was carefully refined so that an Implosion would not occur.
List of Hyperdrive - capable civilizations
It is also believed that some of the Palaedonii Segments are developing Hyperdrive technology.