We present in this thesis a first-principles study on the magnetic properties, the electronic structure and the elastic properties (e.g. bulk modulus) at ambient and higher hydrostatic pressures of 3d metal- based compounds using the well known Full-Potential Local-Orbital minimum basis (FPLO) code. The systems under study are the ferromagnetic element Fe, paramagnetic element Y and the Y-Fe based compounds: YFe2 and the hypothetical YFe5 . The LSDA and GGA approximations, as implemented in FPLO-09 are used throughout the scalar relativistic calculation in this work. This thesis is composed of three chapters, an abstract and a conclusions section. The first one deals with a necessary introduction to the subject, the theoretical background and calculation method are outlined in chapter 2. We present our results in chapter 3 and discuss them in the light of available other first – principles calculations and experimental data.