Series
There are 3 different DB series. Dragon ball, Dragon ball Z, and Dragon ball GT. they were all created by Akira Toriyama except for Dragon ball GT. If you need more info, check out some .
Dragon ball - This is where everything started. The first character we get introduced is Goku. As a little boy, he was living in lonely bush all alone, isolated from the rest of human society. Then Bulma comes along and changes everything. her summer holiday to find the 7 Dragon balls, after she found one in her attic. She takes Goku with her as her body guard and their journey begins. Characters such as Master Roshi, Yamcha, Piccolo, Chi Chi are introduced (and many more) in DB and most of them also appears in DBZ as well. This is much more comical than DBZ with less violence.
Dragon ball Z - After Dragon ball, while everyone thought it was peaceful to live on earth, uninvited guest comes along to visit Goku and his family. His name was Radditz and he claimed to be Goku's brother from Planet Vegeta. he tells Goku his real name is Kakarot and he is Saiyan, the race of fighters. Goku also discovers awful truth that he was sent to Earth as a baby to destroy the planet. More stories about Saiya-jin race is told throughout this series and even more characters are introduced (Vegeta, Trunks etc).
Dragon ball GT - This wasn't created by Akira Toriyama, so graphics and bits and pieces are slightly different if you look closely (e.g Trunks hair color). DBGT is bit weird, and sometimes it is bit off the whole DB theme. Goku turns into a kid and he have to find a black Dragon ball to be a grown up again. So he leaves with Trunks and Pan (his grand daughter, Gohan and Videl's daughter) to find it. This series was only 60 episodes long since it wasn't so highly successful.
Disclaimer: I do not own DB/Z/GT (I wish!!!) and they belong to Akira Toriyama, Bird Studio, TOEI blah, blah, the point is they are under copyright of their respected owners and I have nothing to do with it and I am just crazed fan making website about it. I know no one's going to read this, but just so you know.