This book covers the fundamental theory of stochastic processes for analysing mechanical and structural systems subject to random excitation, and also for treating random signals of a general nature with special emphasis on earthquakes and turbulent winds. Starting with basic probability calculus and the fundamental theory of stochastic processes, the author progresses onto engineering applications: systems analysis and treatment of random signals. The random excitation and response of simple mechanical systems and complex structural systems is discussed in some detail. Extreme conditions such as distribution of large vibration peaks, random excursions above certain limits and mechanical failure due to fatigue are then addressed. The text also offers a discussion of some well-known stochastic models and an introduction to signal processing and digital filters. Numerous worked examples are included: distribution of extreme wind speeds, analysis of structural reliability, earthquake response of a tall multi-storey structure, wind loading of tall towers, generation of random earthquake signals and earthquake risk analysis.