Summary:

Three million years ago, a radiation leak killed the crew of the mining ship, Red Dwarf. The only survivor was Dave Lister, the chicken soup machine repairman. He spends his time on the ship with a holographic projection of Arnold Rimmer (his dead bunkmate), Cat (a life-form that evolved from Dave's cat), Holly (the ship's senile computer), and Kryten (a service mechanoid).

3 Million Years from Earth, the mining ship Red Dwarf
Its crew:
Dave Lister, the last crew member alive
Arnold Rimmer, a hologram simulation of his dead bunkmate
Cat, a humanoid who evolved from Lister's cat.
Additional:
The ship's crew has come across new members:
Kryten, a series 4000 mechanoid rescued from the Nova 5
Navigation Officer Kristine Kochanski, from a parallel universe.
I am Holly, the ship's computer with an IQ of 6000 (and rapidly decreasing). Message Ends.
Welcome to the Red Dwarf guide.
Enjoy the backstory and details of one of the best SF parodies ever created for TV.