This book is for readers who have learned about first order logic; G?del's completeness theorem; the L?wenheim-Skolem theorem; the Tarski-Vaught criterion for being elementary sub-model; and who know naive set theory. A graduate course in model theory will be helpful. The thesis of the book is that we can find worthwhile dividing lines among complete first order theories T; mainly countable. That is, properties dividing them in some sense between...