Holmstrom Model theory

There is at least one introductory Springer book.

Folder: AG/Model theory. Includes the MSRI 39 volume with various survey articles.

http://en.wikipedia.org/wiki/Model_theory

Book: A course in model theory, Poizat

http://mathoverflow.net/questions/7018/model-theoretic-applications-to-algebra-and-number-theoryiwasawa-theory

http://mathoverflow.net/questions/9667/what-are-some-results-in-mathematics-that-have-snappy-proofs-using-model-theory

nLab page on Model theory