This essentially self-contained, deliberately compact, and user-friendly textbook is designed for a first, one-semester course in statistical signal analysis for a broad audience of students in engineering and the physical sciences. The emphasis throughout is on fundamental concepts and relationships in the statistical theory of stationary random signals, explained in a concise, yet fairly rigorous presentation. Fourier series and transforms - fundamentally important in random signal analysis and processing - are developed from scratch, emphasizing the time-domain vs. frequency-domain duality. Basic concepts of probability theory, laws of large numbers, the stability of fluctuations law (central limit theorem), and statistical parametric inference procedures are presented so that no prior knowledge of probability and statistics is required; the only prerequisite is a basic two - three semester calculus sequence. This title features: introduction of the fundamental concept of a stationary random signal and its autocorrelation structure; power spectra of stationary signals and transmission analysis; filter design with optimal signal-to-noise ratio; computer simulation algorithms of stationary random signals with a given power spectrum density; complementary bibliography for readers who wish to pursue the study of random signals in greater depth; and, many diverse examples as well as end-of-chapter problems and exercises. Developed by the author over the course of several years of classroom use, "A First Course in Statistics for Signal Analysis" may be used by junior/senior undergraduates or graduate students in electrical, systems, computer, and biomedical engineering, as well as the physical sciences. The work is also an excellent resource of educational and training material for scientists and engineers working in research laboratories.