Rasengan is one of the most popular Jutsu in Naruto series aside from Shadow Clone. It is also my favorite Jutsu next to Amaterasu. Basically Rasengan is a ball of rotating Chakra held by the user's hand that will dissipate after it hits the target. It is a high rank jutsu because it requires a high level of chakra control in order to create one. With this, it is normally considered as the highest form of Shape Transformation because of its Difficulty and Power. Even Jiraiya said that Rasengan is a stronger Jutsu than Chidori (a Nature Transformation). But still the evolution of Rasengan is still never stop as it is getting passed down to the next generation.
The debate is still ongoing about who is the original creator of this powerful Jutsu. Some people say it's Jiraiya-sensei, some say it's Minato and some claimed it is Ashura. Funny though cause this stupid debate is unnecessary because the answer lies in anime and manga itself.
Creator of Rasengan
The creator of Rasengan is no other than Minato Namikaze. I get it why they still insist that Ashura Otsutsuki is the original creator. That makes them wrong though and you'll know the reason why later.
Rasengan was created by Minato after observing Tailed Beast Bomb for 3 years. So basically Rasengan is a copy of tailed beast bomb. It makes sense how Naruto created Tailed Beast Bomb easily after he got the form of Nine Tails Chakra Mode. Minato intended to create Rasengan to be the highest Form Transformation. But the Rasengan we know is just the first part of Minato's vision of Rasengan. His true goal is combining Form Transformation and Nature Transformation to create the complete and perfect version of Rasengan. This goal didn't succeed because we all know that Minato died at early age. Later his Son, Naruto, completed this one as he successfully added Wind Nature to the Rasengan.
Minato is still the creator of Rasengan. He spend lots of Time imitating Tailed Beast Bomb. He makes the proper procedure on how to perfectly create one. He is also the one who named it "Rasengan" and the one who teaches it to his Master that later being passed to his son. So I guess He really deserve the title as the Creator of Rasengan.
Why Ashura Didn't Get the Credits of Being the Creator of Rasengan
Ashura Otsutsuki - Ashura is the son of Hagoromo Otsutsuki also known as "The Sage of the Six Path". His brother Indra Otsutsuki is the creator of Ninjutsu and the head of Uchiha Clan. Meanwhile Ashura become the successor of his father and Head of Senju clan. The reason why Ashura isn't considered as the creator of Rasengan because what he created isn't actually Rasengan. The Technique he used to cut through the bedrocks while building a well is a type of Wind Release jutsu. Take note that the Rasengan we all know is Ball of pure Chakra (no nature at all). So what Ashura created isn't considered as Rasengan. And that one Jutsu he used to fight against his brother similar to Rasengan is still unknown. It is called as Amenomihashira from a video game though which means "Pillar of Heaven" but the canonical name isn't revealed at all. Sure it may look similar to Rasengan but we don't know if it follow the proper procedure of building the real one. It should be made using Rotation of Chakra, increasing the Power and volume of rotation and Contain it into a form of sphere. Ashura made it looks like Rasengan but it is made in an Unorthodox way. So it is better to be called as a Prototype of Rasengan but not the real Rasengan at all. That's why Ashura didn't get the credit of being its creator.
All Users of Rasengan
So far they are the confirmed persona that can use Rasengan.
Jiraiya
One of the Legendary Sannin and the master of Minato Namikaze. After Minato managed to create Rasengan, the first person he passed this technique is his own master. With the experience and power of Jiraiya, he obtain Rasengan. It is also believed that Jiraiya's Rasengan is powerful enough to crush mountains. It is not a surprise since he also trained in Sage Jutsu. He may possess the most powerful Rasengan next to Naruto. So sad that we didn't witnessed it since he barely get scene and he died during Pain arc.
Kakashi Hatake
Kakashi didn't called copy ninja for nothing. He can actually copy Rasengan and even tried to add lightning nature to it just like what his master did, Minato. Even being a student of Minato himself, it hasn't mentioned that Kakashi learned Rasengan from him. In fact it is not clear how and when Kakashi learned to use this technique. His original technique "Raikiri" was made because of his failed attempt to combine Lightning Nature and Rasengan.
Naruto Uzumaki
Well of course, our very own Ninja that makes Rasengan very famous. Being the son of Minato and the student of Kakashi and Jiraiya, the Rasengan is destined to be learned and be perfected by Naruto. It was proven since he is the very first Rasengan user to successfully add Wind Nature to Rasengan. With this, Rasenshuriken was born and the evolution of Rasengan didn't end with that. With the power of Tailed Beast and Sage of Six Path power he eventually developed this technique to its full potential. Currently he has the most powerful Rasengan.
Konohamaru Sarutobi
Konohamaru admires Naruto so much that he even learned Rasengan so that he can be like him. And ironically, the one who thought Konohamaru how to use Rasengan is Naruto himself. Passing down the Rasengan is also a sign of being the next Hokage. From Minato, Kakashi, Naruto or even Jiraiya (if he just didn't refused the position). Now that Konohamaru mastered this Jutsu that he can make it without Shadow Clone. Is it a sign that Konohamaru will be the 8th Hokage?
Boruto Uzumaki
As expected to the son of Naruto. Boruto eventually learned how to use the Rasengan himself as a test given by Sasuke. Boruto is actually a genius after he learned how to make Rasengan in just 3 days. He also naturally added lightning nature to it without realizing. With that, the Vanishing Rasengan was born. After this ingenious discovery, you can't even imagine that one day Boruto might be able to add two nature to Rasengan cause he can use both Lightning and Wind nature. Vanishing Rasenshuriken will not just be a theory soon.
Evolution of Rasengan
The legacy of Rasengan started by Minato Kamikaze is still evolving as it is being passed down to the next Generation. If it keeps evolving, one day it will be the most powerful jutsu for sure. So let's take a quick look to the evolution of this technique.
Normal Rasengan
This is the base form of Rasengan. It is purely ball of chakra made to add your chakra nature. It was the plan of Minato all along but he didn't even got a chance because he Died. It may be normal but it is still an A Rank jutsu. Which means it is powerful enough even though it is not complete.
Oodama Rasengan
This is the first development of Naruto's Rasengan. It is basically a larger version of normal Rasengan. But seen in its size, the amount of skill and chakra needed to make a humongous one should be impossible. Thanks to the blood of Uzumaki and Nine Tails, Naruto managed to create one. Konohamaru managed to create Oodama Rasengan. Later it developed further into much bigger called Choodama Rasengan (Just like what Jiraiya did on Pain arc and Naruto did on Boruto's Momoshiki arc).
Rasenshuriken
This type of Rasengan is very destructive even to the user. Naruto almost lost an arm after using it. Rasengan is a Jutsu intended to be used in the palm and you need to get into contact to the enemy. With this, the recoil from the destructive force of Rasenshuriken will surely hurt the user. Later, he learned that he can develop it and throw like a shuriken. Naruto even combined Oodama Rasengan and Rasenshuriken making it Oodama Rasenshuriken. It eventually worked and the result is very impressive.
Tailed Beast Rasengan
As I said that Rasengan is based on the Tailed Beast Ball, It is not surprising to evolve it into Tailed Beast Ball itself. It is the evolution of Rasengan where it turn into a small version of Tailed Beast Ball thanks to the Tailed Beast chakra inside of Jinchuriki. It is very destructive type of Rasengan almost similar to the Tailed Beast Bomb produced by the Tailed Beasts themselves.
Vanishing Rasengan
It is first introduced in Boruto and made by Boruto himself. It is a big breakthrough to the Rasengan cause he is the 2nd person to ever add chakra nature to Rasengan other than Naruto. With this, it opens huge room for the development of Rasengan. The Flame Style, Water Style or Earth Style Rasengan isn't impossible anymore. They just need to keep on developing this incredible Jutsu ever made.
Naruto will never be Naruto without Rasengan. And knowing the story of this Jutsu is such an important thing to do. The debate whether who is the real creator of Rasengan should have ended long time ago. They already mentioned it a couple of times in anime. So I hope everything will be clear from now on.
Good writing