I want to learn more about the following Topics:
$q$-analog calculus
what can be done with the $q$-Pochhammer Symbol
applications of $q$-analogs in combinatorics
However, I have found very Little that answers These questions comprehensively. Are there some books or good articles where These Topics are explained?
Every reply will be appreciated.
The bible of $q$-analysis from which I learned the subject is Basis Hypergeometric Series of Gasper and Rahman. It spends some parts on applications in combinatorics.
The book Special Functions of Andrews, Askey and Roy spends a chapter an introduction on $q$-analysis. This is also worth reading.
Be warned that the context of the book Basic Hypergeometric Series is rather dense. It is very hard to read it from cover to cover. If you study $q$-analogues it's often a good idea to also study the classical case too. This makes it much easier to understand what's going on in the $q$-case.
Good luck!