Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: Enrique Casanovas Ruiz-Fornells[en] Boolean algebras are well-known mathematical structures. It is known that the theory of the class of these structures is incomplete, so the aim of this work is to present sistematically the different ways to complete it. In order to do this, we must also study the different kinds of Boolean algebras and their properties. Besides completeness, we also study other questions like ω-categoricity and quantifier elimination. The whole subject is studied in the formal language of first order logic.