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There are many incompatible regexp dialects. This describes one of the dialects, but it doesn't even say which one.

It is full of errors and omissions. It's certainly not "detailed".

I don't recommend this as a learning source. Sorry.

"Just like above example the regular expression ar[.] means: an lowercase character a, followed by letter r, followed by any character."

A period inside a character class is just a period. So that's only going to match "ar."

the example is even worse: the string should match three times, not two. (it misses the a, followed by r, followed by space)

Haven't read the guide, but off the bat it would benefit by at least mentioning the potential for regex with poor performance characteristics or even catastrophic backtracking, and give a few tips on how to avoid them. Neither performance nor backtracking appear in the text anywhere, nor do possessive or atomic.

Word boundaries aren't mentioned either. I use \b quite a bit, was surprised to see it skipped.

Detailed guide on Regex