Introduction to Scientific Machine Learning for Engineering Students offers a first-principles introduction to scientific machine learning for advanced undergraduates, graduate students, and practicing engineers. Using probability theory as the language of uncertainty, it develops a unified framework for modeling, inference, and prediction in engineering systems.The book moves from probability, Monte Carlo methods, model calibration, and Bayesian inference to supervised learning, unsupervised learning, state-space models, Kalman filtering, probabilistic programming, and automated Bayesian inference. Physics-informed machine learning is integrated throughout, emphasizing the combination of data and physical insight.Implemented entirely in reproducible Jupyter notebooks using Python, the text helps readers understand the foundations of modern methods, build models that reflect physical and causal structure, and calibrate them rigorously with data.