In chapter 1, the basic assumptions of the random vibration theory are emphasized. In chapters 2 and 3, pertinent results of stochastic variables and stochastic processes have been indicated. Chapter 4 deals with the stochastic response analysis of single degrees-of-freedom, multi-degrees-of-freedom and continuous linear structural systems. In principle, an introductory course on linear structural dynamics is presupposes. However, in order to make this textbook self-contained, short reviews of the most important results of linear deterministic vibration theory have been included in the start of the relevant sub-sections. Chapter 5 outlines the reliability theory for dynamically excited building structures, i.e., reliability theory for narrowbanded response processes. Finally, Chapter 6 gives an introduction to Monte Carlo simulation methods, which become increasingly important and useful as the computers become more and more powerful.