Rasengan

Rasengan literally means spiraling sphere in English. It is a short range offensive A-rank attack. To use the Rasengan, one must incorporate the chakra control needed for both tree climbing and water walking.The Rasengan is an A-ranked ultra-high-level technique that took the Fourth Hokage three years to perfect, hence, is said to require very high level of chakra control. Unlike the Chidori, the Rasengan does not "cut" per se. It "grinds" rather, literally creating a hurricane of chakra formed in the shape of a small sphere in the palm of a hand, between the size of a softball and a baseball. Upon its collision with a target, the chakra control needed to confine this Jutsu in a small compact spherical form may suddenly be dropped, the effect producing a rather violent explosive effect on the target. Overall, it does have a drawback: the Rasengan needs great chakra control. It is a self-sustaining technique so once the chakra is molded, the user doesn't need to generate any more chakra. This is one of the few jutsu that require no hand seals and can simply be activated with one hand. Something interesting to note is that the Rasengan cannot be copied by the Sharingan because there are no hand seals involved. The Sharingan can only copy jutsus which are performed by hand seals, so that means Naruto could use that attack as many times as he wants and Sasuke could not copy it in battle.

Despite its power, the Rasengan is said to be an "incomplete technique". When training Naruto in using his nature manipulation chakra, Kakashi tells Naruto that the Rasengan is incomplete because it only uses shape manipulation, and not nature manipulation. Kakashi tells Naruto that he, nor even the creator of the Rasengan, the 4th Hokage, was able manipulate both combine nature and shape in the Rasengan. Kakashi continues on and says only Naruto can combine both forms of chakra because he believes that Naruto is the only one capable of surpassing the 4th Hokage.

Naruto's Rasengan Training
To be able to execute the Rasengan, at least as we saw Jiraiya teach Naruto, it is necessary to pass 3 stages. 

Rasengan Stage 1
The first stage in learning to use the Rasengan is chakra control. The user must concentrate his chakra in his hand and make it spin in one direction. To be able to execute that the user must combine the techniques of chakra control that he learned to walk up trees to walk on water at the same time. When Jiraiya taught Naruto, this stage consisted in bursting a water balloon..  ----------------------------------------------------------------------------------------
Rasengan Stage 2
The 2nd stage is said o be 100 times harder than the first. The second level of the Rasengan is power. This level of the technique forces the ninja to focus their chakra to produce a stronger concentration of chakra to add to the spin of their chakra flow. This creates the powerful outward force of the Rasengan, like a hurricane. Powerful, but uncontrollable. Creating a denser chakra is the second step. Jiraiya made Naruto destroy a rubber ball.  ----------------------------------------------------------------------------------------
Rasengan Stage 3
For this 3rd stage, the user must use all that it has already learned in stage 1 and 2. The third level of the Rasengan is dominance. The ninja has to be able to use one hundred percent of their spinning chakra and one hundred percent of their powering chakra, and create a small shell to prevent the chakra from dissipating on contact. In other words, this stage consists of controlling rotation and the power of chakra at the same time in the shape of ball. In this state, the Rasengan maintains a more focused and powerful force. As it meets friction, the chakra is captured and focused by the thin shell driving the force of the chakra into target. When Jiraiya taught Naruto, he made him contain his chakra in the shape of a ball in a water balloon without making it burst.  ----------------------------------------------------------------------------------------

Users of Rasengan

Yondaime, the 4th Hokage
Yondaime is the creator of Rasengan.  

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Jiraiya
Thanks to his pupil, Yondaime, Jiraiya learned the Rasengan. Currently Jiraiya is the best user of Rasengan and was the only person living person that we knew of that could use it (aside from Naruto) until Kakashi showed us that he can use the Rasengan as well.  

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Naruto Uzumaki
After seeing Sasuke use the Chidori at the Chuunin Exams, Naruto wanted Kakashi to teach him to use it as well. Kakashi was not willing to teach Naruto the attack because he felt Naruto was not ready to use the attack because of his lack of Chakra control. Kakashi said that he would teach Naruto only after he had mastered chakra control, so he hired Ebisu to help Naruto control his chakra. Eventually Ebisu was knocked cold by Jiraiya while peeping at girls, so Naruto convinced Jiraiya to teach him to control his charkra. Eventually, Jiraiya also decided to teach him a technique more powerful than Chidori - Rasengan! Naruto succeeds in controlling his chakra and than learned the jutsu in only 3 weeks. Naruto's Rasengan was different from Jiraiya's because he needed the help of  his Kage Bunshin (Shadow Clone) to execute the attack. In extreme emotional states, however, Naruto is able to use the Rasengan without the help of his Shadow Clone.  

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Kakashi Hatake
In chapter 321 of the Naruto manga, Kakashi shows Naruto that he too can use Rasengan. Unlike Jiraiya who just uses one hand and Naruto who uses his Shadow Clone, Kakashi holds his right wrist with left hand and as he is forming the Rasengan.

Different Types of Rasengan

The Rasengan
This version is the most basic form of Rasengan. The user concentrates chakra in his hand and makes it whirl while maintaining it in the shape of a ball. The power of this Rasengan depends on the quantity of chakra that the user uses.  ----------------------------------------------------------------------------------------

The Rasengan Naruto Style
Since Naruto could not initially create and control his chakra using only one hand he had get help from his Kage Bunshin (Shadow Clone) in order to execute the attack. The clone creates the swirls of chakra while Naruto maintains the chakra in a ball.   ----------------------------------------------------------------------------------------

Oodama Rasengan (Great Ball Spiraling Sphere)
A larger and more powerful version of the Rasengan molded using the Nine-tailed fox's chakra. As the chakra is more unstable, he needs a clone to form and control the energy. Naruto uses this Kage Bunshin no Jutsu (Shadow Clone Jutsu) to defeat Yuura (who was acting as Itachi by way of a shape shifting technique). The anime is not up to the point where Naruto uses this so. this attack has only been shown in the manga.