This book is about theoretical physics especially Mathematical Physics in Dynamic. This means the trajectory for any system and its behavior in nature. So, when we know position or trajectory at any time, we can determine everything for this system, e.g. velocity, energy, momentum, pressure, etc. All physical or natural systems are constrained system, except free particles. Newtonian, classically and Quantum Mechanics have Hamiltonian and Lagrangian approach which depend on the energy of the system. From action principle we can arrive to equations of motion from which we can obtain the position or trajectory in any time. It is not an easy task. We can apply this approach for several branches of physics, Electromagnetic, Einstein Gravitational and Field Theory, etc. This book tackles some systems in an approach which is based on Hamilton-Jacobi approach, examine the equation of motion and find out the solution in real physical system. It also tests the validity of this approach on real physical system because its author tests his approach on mathematical models. This book also quantizes the system, since any classical system can be quantized to obtain eigenvalues or energy level.