Here is some books in mathematical logic :

1. General

• H. B. Enderton, A Mathematical Introduction to Logic.
• D. Van Dalen, Logic and Structure.
• I. Chiswell & W. Hodges, Mathematical Logic.
• E. Mendelson, Introduction to Mathematical Logic.
• منطق ریاضی. دکتر محمد اردشیر

2. Model Theory

• C. C. Chang & H. J. Keisler, Model Theory.
• D. Marker, Model Theory An Introduction.
• B. Poizat, A Course in Model Theory.
• K. Tent & M. Ziegler, A Course in Model Theory.
• W. Hodges, Model Theory.
• S. Shelah , Classification Theory.

3. Set Theory

• T. Jech, Set Theory.
• K.Kunen, Set Theory.
• A. Kanamori, The Higher Infinite.
• A. Kechris, Classical Descriptive Set Theory.
• W. Just and M. Weese, Discovering Modern Set Theory (2 vols).

4. Proof Theory

• J. Barwise & J. Etchemendy, Language, Proof and Logic.
• R. Bornat, Proof and Disproof in Formal Logic.
• Handbook of Proof Theory.

5. Computability Theory

• H. Rogers, Jr., Theory of Recursive Functions and Effective Computability.
• E. Griffor (ed.), Handbook of Computability Theory.
• P. Odifreddi, Classical Recursion Theory (2 vols).
• R. Soare, Recursively Enumerable Sets and Degrees.