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...
The playlist is aimed at a general scientific/business audience, the presenter suggests that a lot of natural and business systems can be described in this manner. The presenter also mentions how a Clingo program was used, without modification, to optimize radio frequency band allocation.
Here's a repository [1] of ASP programs in clingo. Under problem classes, I see mostly: game AIs, graph problems, various puzzles, so on.
[0] https://www.youtube.com/playlist?list=PL7DBaibuDD9O4I05DiQfi...