Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2017, Tutor: Joan Soto i RieraThe aim of this project is to construct a complete classification of all possible ground wave functions of a pentaquark consisting of four light quarks and a heavy antiquark. The existence of such a particle has not been established yet, but the theoretical interest in studying properties of pentaquarks has raised since the discovery, in July 2015, of an exotic baryon consisting of three light quarks (two up and one down) and a heavy pair charm-anticharm. We will study the symmetries of the internal degrees of freedom of avour, colour and spin by computing the tensor product of irreducible representations of SU(3) and SU(2), and then identify which results correspond to particles that hold the quark model symmetry principles and thus could exist and might be discovered in the future.