The paper by K. Behrend and B. Fantechi introduces the concept of the intrinsic normal cone for Deligne-Mumford stacks, which is a fundamental tool in constructing virtual fundamental classes for moduli spaces. The authors define the intrinsic normal cone as an algebraic stack over the original stack, which captures the singularities of the stack. They also introduce the notion of an obstruction theory and a perfect obstruction theory, which are essential for defining the virtual fundamental class. The construction of the intrinsic normal cone is divided into two steps: first, they associate an algebraic stack (the intrinsic normal cone) to any Deligne-Mumford stack, and then they define the virtual fundamental class using an obstruction theory. The paper includes examples and discusses the relative case, providing a comprehensive framework for understanding and working with moduli spaces in algebraic geometry.The paper by K. Behrend and B. Fantechi introduces the concept of the intrinsic normal cone for Deligne-Mumford stacks, which is a fundamental tool in constructing virtual fundamental classes for moduli spaces. The authors define the intrinsic normal cone as an algebraic stack over the original stack, which captures the singularities of the stack. They also introduce the notion of an obstruction theory and a perfect obstruction theory, which are essential for defining the virtual fundamental class. The construction of the intrinsic normal cone is divided into two steps: first, they associate an algebraic stack (the intrinsic normal cone) to any Deligne-Mumford stack, and then they define the virtual fundamental class using an obstruction theory. The paper includes examples and discusses the relative case, providing a comprehensive framework for understanding and working with moduli spaces in algebraic geometry.