This textbook aims to equip readers with a deep understanding of mathematical techniques essential for modeling, analyzing, and solving real-world problems across diverse disciplines. Written for graduate students and professionals, the book emphasizes practical applications of applied mathematics in the context of modern challenges, especially in the age of artificial intelligence and data-driven sciences.The text is structured around core areas including complex analysis, differential equations, variational calculus, optimal control, stochastic processes, statistical inference and learning....