Introduction to physcial and mathematical modeling ?? simple models based on mass and heat balance for metallurgical processes ?? numerical methods for solving conduction and fluid flow equations ?? some case studies on mathematical modelling from iron and steel making will be discussed such as modelling of blast furnace, basic oxygen furnace, electric arc furnace, ladle furnace, ingot casting, continuous casting, forging, electroslag refining, sheet metal forming etc. some case studies on physical modelling such as ladle furnace, tundish, continous casting etc.