Applications of mono-anabelian geometry I'm about to start learning some anabelian geometry.
I've come across some papers discussing 'mono-anabelian' geometry. 
I think it sounds interesting.. as I do not yet have a strong background in this field yet, I don't really know what 'mono-anabelian' geometry is able to solve, that "usual" anabelian geometry might not.
So here's the question[s]:
What are the most 'well-known/important' applications of mono-anabelian geometry?
Using the notational conventions of Mochizuki: Are there (interesting) results using mono-anabelian geometry in a way, that seems to be not applicable by 'bi-anabelian' methods?
I'd be interested in papers/articles, keywords to look for etc.
Also: Is mono-anabelian stuff widely 'acknowledged' by the anabelian geometry research community?
As it is related: What would be a good place to start learning about anabelian geometry?
Like: What papers, scripts, books, lecture notes, ...,  could one start looking into?
(Assuming a basic knowledge of algebraic geometry, class field theory, also a really (really!) basic understanding of the etale fundamental group)
 A: Let me remind you the first result in anabelian geometry, i.e. Neukirch-Uchida theorem, which states that: Given an isomorphism of absolute Galois groups of number fields, there exists a unique isomorphism of corresponding number fields. This is a bi-anabelian result, roughly speaking bi-anabelian means that given an isomorphism of two objects and end up with an isomorphism of two objects. Yuichiro Hoshi developed the following result: Given an absolute Galois group of a number field, one can reconstruct the number field by using a group theoretic algorithm. This is a mono-anabelian result corresponds Neukirch-Uchida theorem. So you can regard mono-anabelian result as an algorithm to really "compute" corresponding bi-anabelian result.
Mono-anabelian reconstruction of number fields by Hoshi is about the mono-anabelian algorithm of Neukirch-Uchida theorem, the paper is fairly self-contained, if you know the proof of Neukirch-Uchida theorem, you should not have too much difficulties on this paper.
If you want to start learning anabelian geometry, you should first look at Cohomology of Number Fields by Neukirch-Schmidt-Wingberg, the final chapter gives you a very good introduction of anabelian geometry, and the proof methodologies in bi-anabelian geometry. Technically, after reading the proof of Neukirch-Uchida theorem, you can go to the mono-anabelian result by Hoshi, or go to further generalizations of Neukirch-Uchida theorem, for example the function field case(replace number fields by function fields) or the maximal solvable case (replace absolute Galois groups by its maximal solvable quotients), both generalizations are proven by Uchida.
What I have mentioned are all about the isom-form of anabelian geometry, there are also hom-form, which is much more difficult, a lot of problems have not been solved yet.
I hope this helps.
