This book has two chapters. The first is a modern or contemporary account of stability theory. A focus is on the local (formula-by-formula) theory, treated a little differently from in the author's book Geometric Stability Theory. There is also a survey of general and geometric stability theory, as well as applications to combinatorics (stable regularity lemma) using pseudofinite methods. The second is an introduction to "continuous logic" or "continuous model theory," drawing on the main texts and papers, but with an independent point of view. This chapter includes some historical background, including some other formalisms for continuous logic and a discussion of hyperimaginaries in classical first order logic. These chapters are based around notes, written by students, from a couple of advanced graduate courses in the University of Notre Dame, in Autumn 2018, and Spring 2021.