Learn how to find trajectories with prescribed itineraries in the planar circular restricted three-body problem through this comprehensive tutorial and MATLAB demonstration. Explore numerical methods for generating periodic orbits and their invariant manifolds, focusing on an algorithm to create trajectories with specific itineraries. Follow along with a detailed example computation in MATLAB, demonstrating how to take a Poincaré section of a stable manifold tube on a Lagrangian L1 Lyapunov orbit. Gain insights into differential correction techniques, the use of state transition matrices, and the step-by-step process of constructing complex orbital trajectories. Download the provided MATLAB code to execute the examples and deepen your understanding of advanced orbital dynamics concepts.