This chapter examines the A* algorithm in both theory and practice. It presents core principles and mathematical foundations of this essential pathfinding technique. Implementation strategies and algorithm variants receive detailed attention. We explore practical applications in robotics, gaming, and navigation systems. Memory optimization techniques and performance analysis tools help students optimize implementations. Hands-on Python examples demonstrate algorithm behavior in various scenarios. Students learn to adapt A* for different environments, from simple grids to complex terrain. The chapter covers advanced topics including parallel implementations and integration with modern AI.