There are two Kingdoms of bacteria - Archaea and Eubacteria.
Archaea is more of an "old school" primitive bacteria that live in extreme places (we sometimes call them extremophiles).
There are several types of Archaea, including: Thermophiles (heat lovers), Halophiles (salt lovers), and Methanogens (bacteria living in the digestive tract).
Eubacteria = most every other bacteria type
We can classify bacteria several ways, including by shape and stain color!
By shape: Bacillus: Rod-shaped. Coccus: Spherical. Spirillum: Spiral-shaped.
There are many more GOOD bacteria than BAD bacteria!
Bacteria have many positive uses, including defense against disease/infections, in the dairy industry, etc
