The Cauchy Distribution https://en.wikipedia.org/wiki/Cauchy_distribution is an example of a distribution without mean nor variance nor higher moments. Though I believe mean and median are defined.
Ok, I've gotten into the bad habit of getting into debates in YT, which I'm trying to discipline myself to stop doing. Still, I think I've come up with a good line before leaving any exchange: " Send regards to Mr Dunning and Mr Kruger ".
I personally suggest you browse casually through topics and when you have enough knowledge, you buy the book. Otherwise if you want to go into a book directly, I liked Van Lint and Wilson's book.
Edit: You may get a " Combinatorics lite" book using a Discrete Math book.
Edit 2: Sorry, this book...
Hmm, I was seeing an ad for " When Animals Attack". I can imagine finishing my day eating wings, with an ice-cold beer, watching a snake swallowing up a rabbit whole. Edit: I wonder if it was intended as a joke.