As variability and noise affect all measurements, all signals are inherently a stochastic variable. De-terministic approaches to signal processing are thus inadequate for many real-world applications. Be it a radar signal to detect a plane, an electrocardiogram to diagnose hearth conditions, or a GPS signal to guide an autonomous car, virtually every engineer deal with real-world signals, affected by several sources of noise and interference. Understanding how to handle and process signals in the presence of uncertainty, e.g., “random” signals, is thus fundamental for every student aiming at becoming an engineer. This course provides the basic tools necessary for understanding and processing random signals. The course is divided in three parts and it includes a blend of reading and video materials, quizzes, and assignments. The first part cover topics of probability, random variables and random processes and is a pre-requisite for the following parts. The second part dives into estimation theory and estimation methods including least-square, maximum likelihood and Bayesian estimation; the application of estimation theory in the context of spectral analysis is also discussed. The final part covers hypothesis testing and detection theory, with applications for detecting a deterministic signal in noise.