My favorite introductory book on mathematical logic is Robert S.Wolfe's A TOUR THROUGH MATHEMATICAL LOGIC.Amazingly well written,it covers an extraordinary amount of material in both logic and set theory,complete with biographical vignettes and historical insights.There a deep discussion of first order logic and it's place in metamathematical systems.It also has a wonderful introductory chapter on the theory of computation and it's origins.This is the book I would recommend to any of my students if they asked me about logic.

After that,there are several more advanced texts that I like,particularly the ones by Shoenfield and the classic by my old teacher,Elliot Mendelson.

You can't go wrong with any of those.

My favourite introductory book on mathematical logic is Robert S. Wolfe's A Tour Through Mathematical Logic. Amazingly well written, it covers an extraordinary amount of material in both logic and set theory, complete with biographical vignettes and historical insights. There a deep discussion of first order logic, and it's place in metamathematical systems. It also has a wonderful introductory chapter on the theory of computation and its origins. This is the book I would recommend to any of my students if they asked me about logic.

After that, there are several more advanced texts that I like, particularly the ones by Shoenfield and the classic by my old teacher, Elliot Mendelson.

You can't go wrong with any of those.