Importance of $q$-analog I am currently studying q-analog, but I was actually confused on what its actual purpose is. Like I see all these manipulations using $q$, but I have little idea on what they represent. Sure the series and manipulations they look nice, and work out nicely, but again quite lost on what its actual purpose is. 
I would appreciate some little background information and the actual use and intuitive interpretation of what they represent in mathematics. 


The nice and gentle surveys

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*The q-binomial Theorem by Shaun Cooper


*On the q-binomial coefficients and binomial congruences by Armin Straub
might be helpful. The first presents a connection with enumeration of lattice paths.
The classic

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*Integer Partitions by George E. Andrews and Kimmo Eriksson is the  introductory text to integer partitions for beginners. $q$-related material starts with Chapter 7 Gaussian polynomials.

A book about the  development of $q$-calculus from a historical perspective and providing many examples of applications is

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*The History of q-Calculus and a new method by Thomas Ernst


