Dragon Ball Kai is a shortened version of Dragon Ball Z.
The series takes place 5 years after Dragon Ball. In a world different from ours, Son Goku is a father. He is married to ChicChi and has two sons, Gohan and Goten. His friends, Krilin, Little Heart, Vegeta and Bulma are always with him. The threats are growing. A great alien warrior, Goku can become a super warrior to increase his power. Perhaps considered the best fighter in the universe, he must constantly prove his power during martial arts tournaments or against alien enemies who come to Earth to challenge him. Earthlings are unaware of the presence of superhuman beings like Goku on their planet and are always stunned by their fights.
One day, Raditz lands on Earth and declares that he is Goku's brother. He belongs to the Sayajin people, inter-temporal warriors who put the universe to fire and blood. Their planet, Vegeta, has been destroyed and only four pure Sayajins are left: Goku, Raditz and his accomplices who went on a mission, Vegeta and Nappa. Goku refuses to join Raditz who then decides to kidnap Gohan....
This is where this great adventure begins...