Vertical hoist systems are used for the vertical transport of people and materials. One of the basic performance parameters of the operation of the vertical transport installations is the specific energy consumption during a cycle. It therefore means that the optimization of the transport cycle related to this parameter may be realized using a functional with a function under the integral depending on the electric energy consumption during a race. Another performance of the vertical transport installations is the stability, feature which is that when it is subjected to the action of one harmful size of the moment the system will return in the end at the stationary phase. Thus, the Balance Survey also deals with the determination of variation functions in time of the current of the main actuation motor, of speed when starting the vertical transport installation, as well as the study in time of the variation of speed when applying loading shock. The book is addressed both to the experts in the field, as well as to the students of the Faculty of Mechanical and Electrical Engineering, it consulting may enrich their knowledge acquired in the field of vertical transports.