Maintenance Engineering covers a wide spectrum of maintenance engineering, planning, optimization and relevant decision making approaches. This, being an important issue for any manufacturing industry and production environment, is of high significance to be extended and fostered in the developing countries; where the production equipments are most usually imported and scientific methods and activities of maintenance play crucial role in the smooth running of industries, equipment lifetime and productivity. Basic terms are defined; the necessities for scientific maintenance planning and decision making are explained; mathematical statistics for downtime data analysis are discussed; reliability and maintainability calculus is introduced; inspections and parts replacements optimization methods are considered; optimizing algorithms for production line equipment replacements are shown; system simulations and queuing theory are also considered as approaches to the problem of maintenance system optimizations; and finally, lubrication methods and some case studies are presented.