I read Potassco's Answer Set Solving in Practice book [0] but it's pretty dense. I suspect it would be easier to digest if you read it while also following their course materials, which are all online [1].

These days I recommend people start with the Lifschitz book [2] and read through the Potassco book [0]. Lifschitz's book is a much gentler introduction to ASP and logic programming in general and its examples are in ASP code (not math). It's also more geared towards the programming side than the solving side, which is probably better for most people until they really want to understand what clingo/gringo/clasp are doing and what their limitations are.

There are other more applied courses, like Adam Smith's Applied ASP course at UCSC [3]. The problems in that course look like a lot of fun.

[0] https://potassco.org/book/

[1] https://teaching.potassco.org

[2] https://www.cs.utexas.edu/users/vl/teaching/378/ASP.pdf, https://www.amazon.com/Answer-Set-Programming-Vladimir-Lifsc...

[3] https://canvas.ucsc.edu/courses/1338