Rewriting the documentation of the MIT licensed framework

Does writing a tutorial framework licensed by MIT require written permission?

I want to write a codeigniter tutorial in my language, based on my experience while still referring to the official Codeigniter documentation, is that okay?

The MIT license is very liberal, and says that if you include any such licensed material in your works that you retain the license, and do not claim to have written the material.

If you create new content, independent of our documentation, then you can choose the license of your choice for your material, eg MIT or one of the Creative Commons ones, which could be more appropriate for documentation as opposed to software.

There are a number of translations of the user guide already. The ones I have seen keep the MIT license, and re-use the styles from our docs - basically our docs translated.

not only translations, but also improvised documentation and code additions, and if I publish the tutorial, do I have to include an active link to the reference?

It would be courteous to have a link to the "reference", but not needed. I think it would be hard to talk about CodeIgniter without a link to the downloads, for instance.

Does the MIT license also apply to documentation? or only applies to the "software" framework.?

I don't really understand, the point is I want to make a tutorial site of several frameworks with my own ideas, but a framework of course must refer to the official documentation, is this legal?

The MIT license is intended for software, but can be applied to any creative "work", including documentation.
The Creative Commons licenses are intended for creative "work", which can include software and documentation.

What you are proposing indeed sounds legal.

The MIT license is very liberal, and says that if you include any such licensed material in your works that you retain the license, and do not claim to have written the material.

If you create new content, independent of our documentation, then you can choose the license of your choice for your material, eg MIT or one of the Creative Commons ones, which could be more appropriate for documentation as opposed to software.

There are a number of translations of the user guide already. The ones I have seen keep the MIT license, and re-use the styles from our docs - basically our docs translated.

what the purpose of "independent of our documentation"

Btw, sorry for my bad english... 
I hope you can explain it simply

If you simply translate the user guide, that is not "independent".
If you create your own tutorials, that is "independent".

In the first case, a translation-only would be expected to retain licensing.
In the second case, you can choose the license you feel best.

I made a tutorial based on my knowledge and experience when creating applications with codeigniter, but in writing tutorials sometimes there are some parts that require me to look back (refer) to the codeigniter official documentation, for example, see a list of supported databases, see a list of codeigniter features, etc.

I understand it is quite difficult to determine whether this is independent or not, because the tutorial that I will write is a basic tutorial that might look like the official documentation of CodeIgniter, but I assume that this is not pure translation, but rather improvisation or paraphrasing.

how about that, is it still not independent?

It sounds like you are on solid ground, and should feel free to proceed