Since its birth, Model Theory has been developing a number of methods and concepts that have their intrinsic relevance, but also provide fruitful and notable applications in various fields of mathematics. It is a fertile research area which should be of interest to the mathematical world. This volume should be easily accessible to young people and mathematicians unfamiliar with logic; it gives a terse historical picture of Model Theory; it introduces the latest developments in the area; and it provides "hands-on" proofs of elimination of quantifiers, elimination of imaginaries and other relevant matters. The text is for trainees and professional model theorists, mathematicians working in algebra and geometry and young people with a basic knowledge of logic.