This is a comprehensive presentation of random signals and systems focusing on applications most often encountered in practice, which makes systematic use of geometrical methods, contains an extensive and systematic presentation of covariance matrices, includes a methodical discussion of Gaussian complex random vectors with comparison to the real case and features an elementary presentation of higher-order statistics such as polyspectra, using either moments or cumulants. Use is also made of Hilbert space concepts to clearly explain all the estimation problems by a unified geometrical procedure and provides an extensive and clear discussion of prediction problems, including a detailed analysis of predictable signals and innovations representation.