Abstract: We have been studying the contact equivalence problem of systems of second order partial differential equations for a scalar function and formulated this problem as the Contact Geometry of Second Order. We will discuss two reduction theorems in this Geometry. Utilizing these reduction theorems, we can find many examples of Parabolic Geometries associated with the PD manifolds of second order. As a summary, we will discuss various parabolic geometries of type B₃ associated with the Contact Geometry of Second Order.