Introduction -- Governing Equation of Motions -- Free Vibrations for a Single-Degree-of-Freedom (SDOF) System–Translational Oscillations -- Practical Eigenanalysis and Structural Health Monitoring -- Solving Eigenproblem for Continuous Systems: Rayleigh Energy Method -- Vibration and Buckling Under Axial Loading -- Eigenfrequencies of Non-uniform Beams, Shallow and Deep Foundations -- Deterministic and Stochastic Motions -- Time Domain to Frequency Domain: Spectrum Analysis -- Statistics of Motions and Loads -- Forced Vibrations -- Calculation of Environmental Loading Based on Power Spectra -- Vibration of Multi-Degrees-of-Freedom Systems -- Damping -- Nonlinear Dynamics -- Structural Responses Due to Seismic Excitations -- Fatigue Assessment -- Human Body Vibrations -- Vehicle-Structure Interactions.