Model theoretic Classification Theory, which was initiated by Saharon Shelah, is one of the main themes of research areas of modern model theory. Roughly speaking, Classification Theory can be seen as an attempt to classify "the universe of mathematical structures" according to some existence or non-existence of combinatorial properties of definable sets in their first-order theories. To understand this scheme, we will briefly look at the very basic notions and tools in model theory, and then see some "dividing lines" that distinguish one first-order theory from another. If time permits, we will also have a look at some concrete and familiar examples that satisfy the corresponding theories.