This book explores the reconstruction, extension, and enhancement of the Apollo targeting and guidance algorithms, integrating original guidance concepts with new analytical solutions. It details the Apollo ground-based and on-board algorithms, their iterative targeting procedures, and their performance in post-flight mission reconstructions. The book further introduces advanced real-time targeting methods that improve landing accuracy and autonomy, supporting future robotic and human lunar landing missions. By eliminating iterative computations, these solutions enable real-time re-targeting during powered descent, ensuring safer and more precise landings. This work bridges past Apollo-era methods with modern advancements, making it essential for undergraduate and graduate students, aerospace engineers, researchers, and mission designers.