How can we draw reliable conclusions from limited and imperfect data? This textbook offers a clear and accessible guide to the principles behind scientific inference, showing how a unifying framework connects fields as diverse as Earth science, medical imaging, non-destructive testing, meteorology, climate research, and machine learning. It presents both classical and modern methods for solving real-world inference problems, with practical guidance on evaluating the reliability of results and understanding their uncertainties. Designed as both a learning resource and a long-term reference, the book balances depth with clarity. Hands-on computational exercises throughout help readers translate ideas into practice, strengthen their intuition and build confidence in tackling their own data challenges. It is ideal for advanced undergraduate and postgraduate students, as well as researchers and professionals, across many disciplines, from environmental science and medical imaging to climate research, machine learning, and economics.