Rasengan

The Rasengan is a technique invented by Minato Namikaze, the Fourth Hokage, after three years of development, it was never completed. The Rasengan was meant to be an example of nature manipulation as Minato meant to combine his chakra element with the Rasengan. However, he died before he could accomplish this. Despite this, the Rasengan is still a very useful, difficult to learn, jutsu. As Jiraiya trained Naruto how to use it, learning the Rasengan was broken into three steps. The first was to burst a water balloon by spinning the water inside in multiple directions at once using only the user's chakra, which emphasizes rotation. Then the user needs to burst a rubber ball, and since rubber is thicker and air is completely different from water, it forces the user to use denser chakra to break it, this step emphasizes power. The last is to combine steps one and two by spinning chakra inside a balloon without making it move at all. The Rasengan doesn't use handsigns, it relies only on the chakra control of the user, and once it's complete, it becomes self-sustaining. The chakra spinning at such a speed and compacted into such a small state allows the spinning chakra to grind whatever it comes in contact with, causing major damage to it, and can even cause internal damage. And because the Rasengan is just pure chakra, it doesn't have a definite limit of use like its counterpart, the Chidori. Kyashi, in fact, was able to create an enhanced version of the Rasengan, using Kyosuke's demon chakra.

While the Rasengan is a one-handed technique; in Part I, Naruto has to use three or more hands to use it (Although in episode 112, he is able to create a Rasengan with only one hand, but fails due to Jirobo draining his chakra), mostly due to his poor chakra control. He requires to use of his one hand to create the shell, and a shadow clone's hands to spin the chakra.

While in training, Naruto improved the Rasengan with the Great Ball Rasengan. Later, Naruto mixed his Wind natured chakra to create the Wind Release: Rasengan as it was originally intended. Seireitou Hyuga also succedded in adding fire chakra to his rasengan making it the Katon: Hidama Rasengan. Another variation of Rasengan, is Suiton: Rasentsunami which will create a tsunami when contact is made that is strong enough to brake bones.

Hakushoku Uchiha learned the Rasengan by copying it from Kyūka Namikaze and created from it his own variant.

Itakue yamaki also learned how to use the rasengan after training with the man that saved his life from the fire that destroyed his house and family with further training he learned how to add his earth element to it creating the earth style:crumbling rasengan which would cause stone pillars to jet from the ground and crush the opponent that it hit.

Nine-Tails Influence
When a Nine-Tails Jinchūriki goes into their one-tailed transformation, they are able to make a Rasengan using their hand to spin and the Nine-Tailed Demon Fox's chakra shield to create the shell. Because it is mixed with the demon fox's chakra, the Rasengan had a purplish glow, making it equal in power to Sasuke's Flapping Chidori.