P. Halmos, Naive set theory (Princeton: Van Nostrand, 1965) 
Good introduction to non-axiomatic set theory.
    QA248 .H26, Odegaard

 G. Hunter, Metalogic (Berkeley: U. of CA Press,1973)
A tedious but useful text.
    BC128 .H85 1971a, Odegaard
    
 E. Mendelson, Introduction to mathematical logic, 2nd Edition (Princeton: Van Nostrand, 1979)
More advanced text on the metatheory that we will study.
    QA9 .M4, Math & Suzzallo
 
 R. Stoll, Set theory and logic (San Francisco: W.H. Freeman, 1963)
Not too sophisticated treatment of most topics we will study.
    QA248 .S7985, Math & Suzzallo
    
 J. L. Zalabardo, Introduction to the theory of logic (Boulder, Co: Westview, 2000)
 Covers much of what we will study in a mostly readable way.
    BC108 .Z35 2000, Suzzallo