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Dynamical System is a rich branch of mathematics which is used to study different situations and solve problems with in mathematics and outside mathematics. By the early 20th century, Induced Hyperspace Dynamical Systems was introduced and since then the area is active for progressive research. This book contains a brief survey on Minimal sets and Transitivity further minimal sets, transitivity and orbit sum are studied on the topological groups as base space and on its induced hyperspaces. Many interesting properties are obtained like hyperspace as quotient group, length of orbit segments and many more.