I’m aware of the magic of skein algebras of surfaces only recently. It connects to knot theory in several ways. But while there’s abundance of basic texts on knot theory, I cannot find some for skein algebras.
In this post, I’d like to ask for some basic reference that shows how to compute the ($q$-)Skein algebras of basic examples. For example, the (punctured) 2-sphere and the punctured torus. Thank you in advance.
Actually, it's quite hard to find basic reference to study about these things. At first, you may look at some basic courses about knot theory like https://neil-strickland.staff.shef.ac.uk/courses/MAS344/.
Also, very useful to read papers and survey of experts, e.g Jozef H. Przytycki or Adam Sikora like https://arxiv.org/pdf/math/0602264.pdf or https://arxiv.org/abs/q-alg/9705011
In addition, here is the lecture note about skein theory for quantum GLn