The book "Trajectory Planning for Autonomous Underwater Vehicles" by Clement Petres offers a comprehensive analysis and innovative approaches to trajectory planning for autonomous underwater vehicles. In modern robotics, efficient trajectory planning is crucial, especially in complex and dynamic environments like underwater settings, where currents and non-holonomic movements pose challenges. The work presents a novel approach based on the Fast Marching Algorithm, which takes into account both isotropic and anisotropic media. It explains how the algorithm has been adapted to meet the specific requirements of underwater vehicles to calculate optimal trajectories that reflect real underwater conditions. Additionally, a dynamic version of the Fast Marching Algorithm is developed, allowing for efficient re-planning of trajectories in changing environments. The methods presented have been validated in both simulated and real experiments, highlighting the applicability and robustness of the approaches.