This book presents a study on the vibrations of multistage gear trains. A tractor gearbox with four reduction stages is used as a case study. In order to have quiet and reliable gear trains for automobile and machinery power trains, it is important to optimize the designs based on the gear design parameters which can be easily changed at the design stage, when the cost of redesign is still low. The study presented is based on numerical simulations in which a general code was developed in Fortran Programming language and validated using experimental data obtained from research conducted at the NASA gear research center. Though the study focuses on spur gears, it can be extended to analysis of other types of gears power transmission elements. The study can also be extended to analyse gear trains with different reduction stages.