One of the classical ways to construct moduli space in algebraic geometry is to use group action. This theory was developed by Mumford. This talk is the first of a series of talks on this topic. These talks will basically follow Mumford’s book Geometric Invariant Theory, but more examples and details of construction will be provided. In the first talk, I will introduce group action on schemes, quotients, linearization of a group action, stability, and 1-parameter subgroups. Anyone who has taken Math512 should be comfortable understanding the contents. Cookies will be provided as usual.