The Freeza Series
Dragonball Z returned for another season after the fight against Vegeta. This series, twice as long as the Vegeta Series, caused the popularity of Dragonball Z to skyrocket.

Years ago, Freeza killed Vegeta, the Saiyan king, and conquered the Saiyan Planet. Then, he used the primative Saiyan inhabitants as mercenaries to conquer other planets. Vegeta's son, named after his father, also worked for Freeza despite the fact that he was the Saiyan Prince. A legendary hero rose. His name was Bardock, and his story is told in the Lonely Final Battle. The tragic fate of the Planet Vegeta and the Saiyans were at hand, and only few Saiyans were left now. After the Vegeta Series, only two pure Saiyan breeds were left. One was the Saiyan Prince, Vegeta. The other was Bardock's son, Gokou...
After the death of Raditz, Vegeta learns from the message from Raditz's scouter that Dragonballs existed. Later, he figured out that Namek Dragonballs also existed. After getting beaten by Gokou, Vegeta retreats to Freeza's planet to recover. Now, he carries on the new goal of gathering the dragonballs for himself to be granted the wish of immortality. He also plans to kill Freeza. Freeza is also in search of the Namek Dragonballs to become immortal and begins to terrorize Namek for the dragonballs. Meanwhile, Bulma learns about the Namek Dragonballs PoPo, Kami's assistant. With the hope to gather the dragonballs to wish their friends killed in the Vegeta Series back to life, Gohan, Klilyn, and Bulma venture off to Namek on the spaceship that Kami rode on to travel to Earth years ago. Great battles on Piccolo's home planet are to take place...
Gohan, Klilyn, and Bulma learn that Vegeta is also on Vegeta and also learn about Freeza. Gokou is informed of this and recovers from the battle against Vegeta by eating a senzu bean from Yarijobe. Using Nappa's space pod after it was enhanced by Dr. Briefs, Bulma's father, Gokou travels to Namek. At the same time, the deceased Yamcha, Tenshin-han, Chauzu, and Piccolo are training with Kaiou. Meanwhile, Vegeta begins his fight against Freeza. With strategic actions, Vegeta kills Dodorian and Zarbon, Freeza's right and left hand men, and steals the captured dragonballs from Freeza. However, Vegeta learned from Dodorian that the Saiyan planet was not destroyed by a meteor as stated, but by Freeza. Ambitions to kill Freeza are strengthened. Freeza learns of Vegeta's betrayal and calls forth the Ginew Squad. Team Ginew, consisting of five members who constantly pose in funny dances, have a reputation as being powerful warriors of destruction.
Gokou finally lands on Namek. The Z warriors now have a new enemy, one who must be defeated for the safety of the entire galaxy. Everyone plans to defeat Freeza, but Freeza is too strong. Realizing that he himself cannot defeat Freeza, Vegeta joins the Z warriors, but boasts that it is only to insure that Gokou survives the battle so that he could kill him personally. (However, Vegeta ends up marrying Bulma, and Bulma gets pregnant a son that would become known as Trunks.) Team Ginew is killed by the combined forces of Gokou and Vegeta (except for Ginew, who accidently turned into a frog when he tried to swap bodies with Vegeta and Gokou threw a frog in his path). Then, follows the fights against Freeza himself. To everyone's surprise, Freeza has the ability to transform into a few stages. With each pysical transformation, Freeza's power increases. Klilyn is killed in battle and Gokou becomes enraged in an anger so deep that he too undergoes a transformational powerup. Gokou's hair becomes golden and spikes up, and he reaches Super Saiyan level for the first time. The tides of battle now turn to Gokou. With a single energy blast, Freeza and his planet are blown. Freeza learns the true powers behind a Super Saiyan.
The Z warriors are back on Earth. The dead Z warriors are granted back to life. Everyone thinks that Gokou was killed in battle, but Gokou really escaped to planet Yardrat, where he learned how to teleport. Cold, Freeza's father, learns about Freeza's defeat and quickly gathers Freeza's body parts, which are floating around in space. His henchmen quickly re-ensemble Freeza. (This is why Freeza was half robotic.) Freeza tells his father about Gokou and his powers, but his father doesn't believe him. Cold continues to boast that he is the universe's strongest warrior and best space conquerer, and can never be defeated.
The villains land on Earth to seek revenge for Freeza's defeat. The Earth becomes endangered once again. All of a sudden, a figure appears out of nowhere. It is adult Trunks, but no one knows who he is or where he came from. He turns into his Super Saiyan level and aids the Z Warriors in their battle. Trunks single-handed kills Freeza and Cold with the aid of his sword. Trunks introduces himself as Bulma and Vegeta's son. He grew up and traveled back in time to prevent his chaotic future. Trunks tells about deadly androids. He carries heart attack medicine for Gokou. Trunks also tells that Gokou is not dead, but will appear in front of them in a matter of minutes. Everyone doubts whether or not to believe this stranger. In a few minutes, Gokou really teleports back to Earth in front of everyone and meets Trunks.
This story is continued in the next Dragonball Z series--the Cell series To learn more about Trunks, read about Trunks Story

Notes:

Gokou: Looks the same as he did in the Vegeta Series. However, he is able to turn into his Super Saiyan form 1 in this series!

Gohan: is the same height as Klilyn now and has a mushroom haircut. (not strong enough to reach Super-Saiyan mode yet)

Klilyn: Looks the same as in the Vegeta Series.

Piccolo: Is officially one of the good guys now. (still no change in appearance)

Vegeta: Begins to turn good, but doesn't admit it. He uses the excuse that he is only aiding Gokou so that Gokou will live long enough for him to kill Gokou personally. (does not turn Super Saiyan yet) By the end of this series, Vegeta begins to settle down his space conquering adventures and no longer becomes a threat to Earth. However, his is extremely jealous that Gokou and his own future son has the ability to turn Super Saiyan; he wanted to be strongers. Afterall, he was Prince.

Trunks: Bulma and Vegeta's son. Because his father has black hair and his mother has blue hair, Trunks' genes gave him purple hair. Trunks comes from the future to save Gokou in an attempt to alter his future. Trunks is a cool looking character with a split haircut. In his timeline, he learned how to turn Super-Saiyan.

Freeza: galaxy conquerer. He killed King Vegeta, the king of the Saiyans, and took over Planet Vegeta, where he used the Saiyans as mercenaries. Then, he killed Bardock and destroyed Planet Vegeta. Freeza can change into a few forms before reaching perfect form, but he finally is killed by Trunks. Garlic Jr. made a brief appearance in this series. He escaped from the portal of nothingness, but was defeated and entrapped again.