Unpublished Math 712 notes by Professor David Kueker for the course are here.
Unpublished Math 713 notes by Professor David Kueker for the course are here. Note: The actual text begins on page 27.
Other possible texts
Boolos and Jeffrey, Computability and Logic
Enderton, A mathematical introduction to logic
Chang and Keisler, Model theory
Carol Wood's slides on the definability of Z in Q Summary on slides 7-9.
Julia Robinson's original article (1949).
David Pierce's writeup of the Strong undecidability of C(t1,t2).
Why number theorists will never be happy.