Saiyans are a powerful race of half-ape half-human (in appearance only) aliens from Planet Vegeta. They are very battle hungry creatures and are very powerful. They are capable of using energy at a young age as well as flight and other things natural only to the most powerful of races (such as Changelings and Namekians). They are also the only race capable of turning into the legendary Super Saiyan.
Saiyans look just like humans except they have long monkey tails. The tail grows back though!
A Saiyan when greatly angered can become a Super Saiyan. This power gives the user golden hair, green eyes, and amazing battle potential. This does not end there, though. Upon mastery, a Saiyan can reach up to 7 levels.
The second level of Super Saiyan. This one is the stage directly after Super Saiyan. It gains electricity.
The third level of Super Saiyan. This one is the stage directly after Super Saiyan 2. It gains really long hair and loses their eyebrows.
The fourth level of Super Saiyan. This one is the stage directly after Golden Oozaru. This gains kinda' long black hair and gains red fur. They also regain their eyebrows but gain red rings on their eyes.
The fifth level of Super Saiyan. This one is the stage directly after Super Saiyan 4. This gains longer white hair and lots of muscles.
The sixth level of Super Saiyan. This one is the stage directly after Super Saiyan 5. This gains a yellow spot of hair at the top of their head.
The seventh level of Super Saiyan. This one is the stage directly after Super Saiyan 6. This gains entirely yellow fur and hair and tail.
The eighth level of Super Saiyan. This one is the stage directly after Super Saiyan 7. This gains hair that's pinkish with darker pinkish tips and his tail is dark orange. Their fur is also gone replaced with dark orange runes on his body. Their aura is replaced with electricity and eight diamond like glowing glyphs while his beams are orange in color.
The ninth level of Super Saiyan. This one is the stage directly after Super Saiyan 7. This gains hair is dark purple blue. It's back to being the ength of a Super Saiayn 3's and all of his fur and runes are gone. He still doesn't have an aura and lightning strikes around him when he charges.
The tenth level of Super Saiyan. This one is the stage directly after Super Saiyan 9. This gains hair is short and grey, but he is hairy all over his body. It also gained a lot of muscles, looking like a small grey Oozaru.
Unlike Super Saiyan, it is not an alternate form of the transformation. Instead their eyes go all white and he becomes so angry he loses control of himself. This causes them powerlevel to rise and unlocks different Super Saiyans at an alarming rate. Aside from the white eyes, there is no difference between Enraged Saiyan and regular Saiyan. They can also be any Super Saiyan form while en Enraged Saiyan, the only difference is he gets completely white eyes. He gained this form after suffering from extreme sorrow and anger after losing everyone he cared about to dark TRUNKS.
Goku, also known as Kakarot, is the first Saiyan on Earth. He was sent there when Planet Vegeta was blown up. He was raised there and thought he was a human at first. He is also the most powerful Saiyan and mastered the most Super Saiyans.
Vegeta is the price of Planet Vegeta. He is the second strongest Saiyan alive and is constantly rivaling Goku to be the strongest.
Gohan is the half-Saiyan son of Goku. He is the third strongest Saiyan alive and is also the only Saiyan to be Ultimate.
Goten is the half-Saiyan son of Goku. He is the fourth strongest Saiyan alive.
Bardock is the father of Goku and probably the strongest Saiyan dead. He was super spirit killed by dark TRUNKS, though, so he is permanently gone with no chance of being alive or dead ever again.