I like The Mathematics of Logic by Richard Kaye. A rather unusual approach apparently intended for college math majors, maybe not for everybody. But I am not

I like The Mathematics of Logic by Richard Kaye. A rather unusual approach apparently intended for college math majors, maybe not for everybody. But I am not a math major and it appealed to me. https://web.mat.bham.ac.uk/R.W.Kaye/logic https://web.mat.bham.ac.uk/R.W.Kaye/logic (not very helpful, lots of broken links, just look at the book instead) I also like Logic in Computer Science by Huth and Ryan, cited in another comment here. It is much more comprehensive and has a lot more about logic applications in computer science.