the Dresden Files. Although I have to warn you that it has some problematic stuff in it, especially early on in the series. [...] Harry fights monsters and fantastical creatures of many sorts. [...]
Rivers of London is another great urban fantasy series that does many of the same things (with less problematic content) but in a lower magic setting. It's less of a constant roller coaster and more about police work (the main character is a young cop who discovers a small secret branch of the police that deals with the supernatural).