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.