This book aimed to identify the history of polyamorism in Brazil, as well as the rules that should guide the formalization of the union of this form of family constitution. This study used the inductive method, which allowed to demonstrate the legality of polyamorous unions in the Brazilian legal system, in addition to bibliographic research and indirect research (doctrine and case law). Initially demonstrating the evolution of the family until current times. After these analyses it was sought to clarify the possibility of family constitution beyond monogamy demonstrating the need for ampliativa interpretation of the right put, beyond the minimum state intervention in the right of the families, with the valorization of the right to the search to the happiness. At the end is presented issues related to "polyamory" to finally demonstrate the possibility of generating effects, of personal order.