This thesis is developed in the area of combinatorial algebraic structures on planar binary trees, particularly, combinatorial Hopf algebras.In 1995, Claudia Malvenuto and Christophe Reutenauer introduced a graded Hopf algebra, denoted by GSym, on the graded vector space spanned by permutations. It is called Malvenuto-Reutenauer Hopf algebra or simply the Hopf algebra of permutations (see [MR95]). Later, in 2001, Gerard Duchamp, Florent Hivert and Jean-Yves Thibon proved that the dual structure of the Malvenuto-Reutenauer Hopf algebra SSym∗ can be realized as a Hopf subalgebra of the free associative algebra k[A∗] for some nonempty totally ordered set A, this Hopf algebra is called the algebra of free quasy-symmetric functions and is denoted by FQSym, so that GSym and FQSym are isomorphic Hopf algebras (see [DHT01]).Moreover, in 1997, Jean-Louis Loday y María O. Ronco introduced a newgraded Hopf algebra, denoted by PBT, which is spanned by all planar binarytrees and is called the Loday-Ronco Hopf algebra or simply the Hopf algebra of planar binary trees (see [LR98]), they proved that this algebra is a Hopf subalgebraof the Malvenuto-Reutenauer Hopf algebra, i.e. they defined an injective Hopf algebra morphism PBT →֒ GSym. In 2005, Florent Hivert, Jean-Christophe Novelly and Jean-Yves Thibon proved that the Loday-Ronco Hopf algebra PBT can be realized dually as a Hopf subalgebra of the algebra of quasy-symmetricfunctions PBT ≃ PBT∗ →֒ FQSym, using the theory of search binary trees(see [HNT05]).In 2011, Samuele Giraudo, doctoral student of Jean-Christophe Novelli and Florent Hivert, considered the vector space spanned by Baxter permutations, which is denoted by TBT and is called Baxter Hopf algebra. Samuele Giraudo also proved that the Baxter Hopf algebra can be realized as the Hopf algebra apanned by pairs of twin binary trees (see [Gir11]), which is a Hopf subalgebra of the algebra of free quasy-symmttric functions. So we get that PBT∗→֒ TBT →֒ FQSym.The aim of this thesis is to study the dual structure of the Baxter Hopf algebra TBT∗. In order to do that, we introduce a new class of planar binary trees called Baxter binary trees and prove that TBT∗ is the Hopf algebra spanned by the setof all Baxter binary trees. The underlying vector space has a natural structure of free 2-associtive algebra denoted by BBT, so that TBT ≃ BBT as vector spaces. Identifying both spaces, we get PBT →֒ BBT →֒ GSym. We introduce a dual Baxter congruence, denoted by ≡B∗, and we determine an algorithm, calledBaxter-tree algorithm, to compute related planar binary trees, by this dual Baxter congruence. Finally, using that BBT is a free 2-associative algebra, we generalizethese results to algebras of some nonempty set X, denoted by BBT(X), which we call the algebra of Baxter binary trees of X.PFCHA-BecasMagister en Ciencias Mención Matemáticas60p.PFCHA-BecasTERMINADA