Super Saiya-Jin 1
This level was first reached by Son Goku. He reached this level when he was fighting freeza on planet namek.The death of his best friend krillin finally lit a spark and this forced him to transform. The way to become a super saiya-jin is to have a pure heart and to be very, very angry. Also you have to have more power than a regular saiya-jin. When Goku became SSJ1, his muscle strenth and muscle tone became much larger. His speed also increased. As a side affect, his hair turns yellow and his eyes turn green. Also the Ki is yellow instead of white. This happened in Dbz Episode 95.
This level was first reached by Son Goku. He reached this level when he was fighting freeza on planet namek.The death of his best friend krillin finally lit a spark and this forced him to transform. The way to become a super saiya-jin is to have a pure heart and to be very, very angry. Also you have to have more power than a regular saiya-jin. When Goku became SSJ1, his muscle strenth and muscle tone became much larger. His speed also increased. As a side affect, his hair turns yellow and his eyes turn green. Also the Ki is yellow instead of white. This happened in Dbz Episode 95.
Well, this isn't really considered a real level, this level is really between a Super Saiya-jin 1 and a Super Saiya-jin 2. This was first reached by Future Trunks in the battle when he was fighting Perfect Cell. This occured because he was watching Cell beat his father and because Cell wanted him to power up to his maximum. This caused his muscle tone and stength to get much larger but this also caused the body to become bulky causing him to be much slower. Goku and Vegeta knew about this so they did not use this level against any opponents. This happened in DBZ episode 163.Super Saiya-Jin 2
This level was first reached by Son Gohan in the battle with Cell. When Cell stepped on Android 16's head and killed him, this made Gohan release his anger and made him turn Super Saiya-jin 2. The difference between ssj1 and ssj2 is that ssj2 has everything that ssj1 has but more such has his hair become longer and steater. His muscle tone and stegnth got larger. Also his speed incread. It is easy to tell the difference between ssj1 and ssj2 becuase SSJ2 Gohan has electricity around his body. This happened in DBZ episode 185.
This level was first reached by Son Gohan in the battle with Cell. When Cell stepped on Android 16's head and killed him, this made Gohan release his anger and made him turn Super Saiya-jin 2. The difference between ssj1 and ssj2 is that ssj2 has everything that ssj1 has but more such has his hair become longer and steater. His muscle tone and stegnth got larger. Also his speed incread. It is easy to tell the difference between ssj1 and ssj2 becuase SSJ2 Gohan has electricity around his body. This happened in DBZ episode 185.Super Saiya-Jin 3
This level was first witnessed by Son Goku in the battle with Majin Buu. Goku had learned how to turn Super Saiya-Jin 3 when he was training in heven but it just took him a while to turn SSJ3 on earth. SSJ3 has everything that SSJ2 has and more. His hair becomes really really long. His muscle tone and strenth has greatly increased from SSJ2 . As the same with his speed. This was the highest form of a Super Saiya-Jin in Dragonball Z. Although it is really powerful, Goku did not like to use it because on he loses his energy much faster when he uses this form. When Gotenks goes SSJ3, he does not have this problem. This happened in DBZ episode 245.
This level was first witnessed by Son Goku in the battle with Majin Buu. Goku had learned how to turn Super Saiya-Jin 3 when he was training in heven but it just took him a while to turn SSJ3 on earth. SSJ3 has everything that SSJ2 has and more. His hair becomes really really long. His muscle tone and strenth has greatly increased from SSJ2 . As the same with his speed. This was the highest form of a Super Saiya-Jin in Dragonball Z. Although it is really powerful, Goku did not like to use it because on he loses his energy much faster when he uses this form. When Gotenks goes SSJ3, he does not have this problem. This happened in DBZ episode 245. 
This level was first reached by Son Goku. This happened in the battle with Bebi in Dragonball GT, which was not created by Akira Toriyama like Dragon Ball and Dragon Ball Z. To reach SSJ4 for the first time, Goku had to turn Golden Oozaru (also know as ssj oozaru). He did this after the Kaioshins pulled out his tail and he saw the full Earth (He used the Earth as a moon). Goku went on a rampage, but Pan's tears made him calm and he turned Super Saiya-jin 4. This time, he had black hair with reddish fur on his body and he somehow acquires new clothing. His muscle tone, strength, and speed has greatly increased form the form of SSJ3 and golden oozaru. He also does not have the same energy problem that he had as an SSJ3. This is the highest level of Super Saiya-jin in all three of the Dragonball series. This happened in DBGT episode 35.