Traditional signal processing and machine learning methods rely on mean square error, which becomes brittle when data contains heavy-tailed noise, impulsive disturbances, and outliers—conditions frequently encountered in real-world applications. This comprehensive guidebook introduces correntropy-based methods that demonstrate superior robustness across diverse engineering domains, progressing from foundational concepts to applications. Authored by pioneers in information theoretic learning, the book systematically covers correntropy fundamentals, adaptive filtering techniques, neural network training, feature learning, and applications including point set registration, matrix completion, and federated learning. Each chapter balances rigorous theory with practical algorithms and performance comparisons against conventional methods. With implementation guidelines and a unified framework connecting different robust learning criteria, this book addresses the critical gap between Gaussian-assumption theory and non-Gaussian reality, providing researchers and graduate students with applicable solutions for challenging real-world problems.