This is an introductory course on vibrations and its applications, including computational methods. In addition to providing a comprehensive theoretical background on vibrations of lumped-parameter systems and simple distributed-parameter systems, the course will make an extensive use of commercial finite-elements software for modeling and simulations of realistic mechanical systems. Experimental demonstrations of various vibrations phenomena will also be included. The theoretical treatment will focus on linear systems, and will include modeling of single- and multi-degree-of-freedom systems; normal-mode analysis including natural frequencies and mode shapes; free and forced vibrations; frequency-domain analysis; vibrations of simple continuous systems such as strings, beams, rods, and torsional shafts. The course is intended for graduate students and for undergraduate students with substantial mastery of core undergraduate subjects in mechanics and mathematics.