The Crank-Nicolson (CN) method is a fashionable time integrator for evolutionary partial differential equations (PDEs) arisen in many areas of applied mathematics, however since the solution at any time depends on the solution at previous time steps, thus the CN method will be inherently difficult to parallelize. This talk consists of two parts. In the first part, we consider a parallel approach for the solution of evolutionary PDEs with the CN scheme. Using an allat-once approach, we can solve for all time steps simultaneously using a parallelizable over time preconditioner within a standard iterative method. Due to the diagonalization of the proposed preconditioner, we can minutely prove that most eigenvalues of preconditioned matrices are equal to 1 and the others $z\in\mathbb{C}$ have the model with 1/(1 + α) < |z| < 1/(1 - α), where 0 < α < 1 is a free parameter. Meanwhile, the efficient and parallel implementation of this proposed preconditioner is described in details. Finally, we will verify our theoretical findings via numerical experiments. This is the second part of talk.