This is an introductory course in vibrations and structural dynamics. Vibrations are frequently observed in mechanical (e.g., automobiles, robots), aerospace (e.g., airplanes, satellites), civil (e.g., buildings, bridges), and biological (e.g., eardrum, myocardial cells) systems. As such, modeling, analysis, experimentation, and control of vibrations are critical for many systems. This course covers fundamental concepts on vibrations of simplified (single- and multi-degree-of-freedom lumped-parameter models) and distributed-parameter systems (strings, beams in bending and torsion). Various applications of vibrations are analyzed. An overview of vibration testing and experimental modal analysis is also provided. The topics include free and forced response of single- and multi-degree of freedom structures; harmonic response analysis; vibration suppression; Lagrange's equations to derive the equations of motion; vibrations of strings and beams; and numerical methods to determine natural frequencies and mode shapes.