This chapter describes in detail the formalism of the Generator Coordinate Method and its use in constructing both static and dynamic collective states of the nucleus, starting from constrained Hartree-Fock-Bogoliubov solutions. The full formalism is then reduced to a Schrodinger-like equation, and the calculation of its inertial tensor and zero-point energies is presented. Next, the calculations are extended beyond the adiabatic approximation and the Schrodinger Collective Intrinsic Model is derived. The multi-\(O\left (4\right )\) schematic model introduced in Chap. 2 is used throughout this chapter to illustrate the formalism.