A unified and systematic optimal control theory for nonlinear Cahn-Hilliard equation is perfectly established by the means of distributed control, boundary control and initial control for abstract integral cost function and quadratic cost function in the framework of variational method in Hilbert space under weaker assumptions on exponent of nonlinearity. Computational approach is configured for semi-discrete algorithm (time-continuous, spatial discrete), and is performed using finite element method and updated conjugate gradient method to one-dimensional distributed control case. Parameter identification is slightly touched for unknown parameters appeared at damped and dissipative C-H equation. According to introductory function analysis and physical background, a path way from applied mathematics to control theory is in this monograph for solidly supporting a true solution of optimal control to a broad class binary systems describing by Cahn-Hilliard equation.