The quotient of a scheme by a group action may not exist in the category of schemes. However, it can be described as an algebraic stack. An algebraic stack is a functor from the category of schemes to the (2-)category of groupoids which satisfies some gluing conditions.

In this introductory talk, I will follow the book <Algebraic spaces and stacks> and introduce the definition of algebraic stacks. I will also talk about the ‘orbifold like’ objects called Deligne-Mumford stacks and give some examples of them including the moduli stack of curves of genus g. I will try to cover the quasi-coherent sheaves if time permits.