Mad Jack was an elderly, male, human, first seen in Magyk. A his name implies, he was considered mentally unstable and is noted to have had something of an obsession with rats.
Mad Jack mades a living by cutting reeds for the thatching of roofs. This business would seem to be lucrative, thatched roofs are used throughout The Small Wet Country Across the Sea - they have been seen in the Castle, the Port, The Farmlands, and the Sheeplands -, we know that he makes multiple deliveries in a day - when we first meet him, he is returning from his final delivery of the day -, his supply of reeds is unlimited, and - as cutting, wild growing, reeds is entirely free - he makes 100% profit. However, the reality is rather different; Jack lives in a one room hovel on the edge of the Marram Marshes which he shares with his donkey and he seems to live on withered apples.
At one point in his life, Jack may have been married, certainly a Witch named Linda from the Port Witch Coven appears to be his daughter - she has a love of rats which she apparently inherited from her father. However, the woman with whom he parented his child has - by the time of Magyk - either died, left him, or both - by this point of his life he lives alone with only a donkey and an occasional rat for company.
Jack's madness does not affect his ability to function in day-to-day life, he was able to procreate and is self sustaining, however it manifests itself in his unusual speech pattern - which involves frequent use of the Third-Person perspective when talking about himself - and an unhealthy obsession with rats - whom he considers to be good company. He has been known to take in rats and hold them prisoner, Jenna and Nicko Heap reported that they saw many dead rats in cages inside Jack's shack, which is pretty much kidnap - considering rats in Septimus's world are pretty much as intelligent as humans. One of Jack's most notable captives, and the only one known to have survived the ordeal, was the Message Rat Stanley, who was able to escape by starving himself until he was thin enough to slip through the bars.
Mad Jack does not appear after Magyk, but is referenced.