(1) "Elements of Set Theory" by Herbert B. Enderton
(2) "A Mathematical Introduction to Logic" by Herbert B. Enderton
(1) includes a naive set theory and an introduction of an axiomatic set theory. Enderton's expository style of (1) is accessible to students without having much mathematical maturity. I purchased a used book of (1) from Amazon.com and it has been a good reference for set theory so far.
Even though the title of (2) includes an "introduction", it was not an introductory text for me.
Exercises were challenging and the expository style is very terse in comparison to (1). The book requires some algebraic backgrounds (free group, automorphism, etc) as well.
If you are a graduate student of mathematics, I think the book (2) would be a nice choice for studying mathematical logic. If you are an undergraduate student of mathematics or a graduate student of other areas (physics, computer science, etc), this book would be a bit challenging to you. Anyhow, this book would be still worth reading if you skip some of tough sections and follow the sentential and first order logic part of the book, which is my approach to this book.