This is a book written by someone who is clearly not only a master of the technical details of mathematical logic in the Godelian tradition, but is also well aware of the difficulties faced by the struggling student, who may be coming to grips with very complex ideas for the first time.
Most books on logic (or on mathematics generally for that matter) that achieve any level of technical difficulty are like a sat-nav system that tells you "turn right", "turn left" etc without explaining where you are actually going to, or why you are doing it. Smith's book by contrast is "readable" in the sense of carrying the reader along with constant explanations of where the text is going, and what is the point of the current proof. It motivates the student to keep going like no other text I have come across. I would say it is an essential companion volume for anyone who has bought Mendelson's famous book on mathematical logic, which scores highly on accuracy and completeness and very low on comprehensibility. Together they probably answer most questions a second level student will probably want to know.