The Skyrme model is an effective theory for the description of nucleons, nuclei and pions,where the primary degrees of freedom are mesons and the hadrons and nuclei appear astopological solutions of such model. Furthermore, the number of baryons is identified withthe topological charge of the solitons. The Skyrme model allow us to study hadrons andnuclei starting from a field theory instead of the more common nuclear models based onmethods of the quantum mechanics with a finite number of degrees of freedom. The highlynon-linear character of such field theory makes it very suitable to the description of complexphenomena of strong interaction and very present in several applications. In fact, using theSkyrme model, a lot of nuclear properties can be understood from a qualitative point of view,like their masses, or their spectra (corresponding to excitations of the spin and isospin of theSkyrmions). On the other hand, the quantitative precision of the standard Skyrme model doesnot exceed a 10-30%. The main reason for this limitation is the lack of BPS solutions in thestandard Skyrme model, what implies binding energies too high and internuclear forces toostrong, among other problems.To deal with these limitations, some generalizations of the Skyrme model have beenstudied with the same content of fields but adding new terms to the Lagrangian. Among thesegeneralized Skyrme theories, an integrable theory with an infinite number of exact solutions(topological solitons) saturating a Bogomolny bound has been found out recently. This is theBPS Skyrme model. Due to its integrability, this model has the symmetries of anincompressible fluid. This and the BPS property make the model phenomenological suitablefor nucleus description. For instance, because of the BPS property, binding energies ofclassical solitons are zero, and low binding energies of real nuclei are obtained by quantumcorrections and by small contributions from additional terms in the Lagrangian. Soliton radiialso grow with the cube root of the baryonic charge, as in real nuclei.With the purpose of studying in detail the BPS Skyrme model and its application tohadronic and nuclear physics, the following research lines have been developed:1. The analysis of the thermodynamics of the BPS Skyrme model at zero temperaturewith the introduction of an external pressure and the calculation of the energymomentumtensor. Moreover, two important thermodynamical quantities like thecompressibility and the baryon chemical potential were studied.2. The introduction of the quantization of the collective coordinates (spin and isospin),as in the standard Skyrme model. Moreover, the electrostatic energy (Coulomb term)and a little explicit breaking of the isospin were added. The Coulomb term is reallyimportant for heavy nuclei, whereas isospin symmetry breaking will split the protonsand neutrons.3. The coupling of the BPS Skyrme model to gravity to describe neutron stars in goodagreement with the observational constraints concerning mass and radius. Here, twodistinct approaches were followed (exact and mean-field calculations) finding that,although for global properties there are not too much difference, it is not the case oflocal ones, where the difference is pronounced.4. The study of the influence of several different potentials in the researches mentionedabove, because the specific shape of the potential is not important for themathematical properties.Finally, it is worth commenting that, although the BPS model gives the dominantcontributions to many nuclear matter properties, some evidences have been found that anextension to a near-BPS model is needed for a complete description of strong interactions.