I'm going to talk about the paper, "Basic Concepts of Abstract
Interpretation"(by P. Cousot and R. Cousot).

This paper introduces basic concepts of abstract interpretation
framework. Program is formalized as a transition system and its concrete
semantics is defined as partial trace semantics. Then the authors of the paper
develop the three different abstract semantics of partial trace semantics -
a. reflexive transitive closure semantics, b. reachability semantics,
c. interval semantics. For each abstract semantics, they develop the Galois
connection between concrete semantics and show that each can be expressed in
fixpoint form.

Concepts of widening and narrowing are provided with examples. Then, composition
of three abstractions and hierarchy of four semantics are explained.