Overview
Hoshi no Kirby (星のカービィ, Hoshi no Kābī, lit. Kirby of the Stars) is what the Kirby series name is in Japan as well as the first game's name in Japan.
For the first game see Kirby's Dream Land
Series
The first work that utilized Kirby's round design and treated Kirby as a ball was Kirby's Adventure. The first work that adopted a game system that used Kirby as a spherical object was Kirby's Pinball Land. Basically, all the games in the series are set in parallel worlds that are independent of each other.
The numerical series of Kirby's Dream Land 2, Kirby's Dream Land 3, and Kirby 64: The Crystal Shards is a kind of offshoot of the Kirby series in that they share the same system and story, and the original author, Masahiro Sakurai, was not involved in the planning of the series. Some fans say they like this one better because it still retains the old Kirby look.