In this thesis, non-collinear magnetism has been studied by using density functional theory and the augmented plane wave method with local orbitals (APW+lo). Two conditions for non-collinear instabilities have been identified in this thesis. First, the Fermi energy should cut through both spin up and down states. Secondly, strong nesting between the spin up and spin down Fermi surfaces is needed. The two criteria described here can be fulfilled by tuning the exchange-splitting and/or by modifying the volume. Calculations on several elements; bcc V, bcc and fcc Mn, bcc Fe, bcc and fcc Co, and bcc and fcc Ni show that a non-collinear state can be stabilized provided that the criteria discussed above are met. More complex materials have also been analyzed in terms of these two criteria. The substitutional alloys TlCo2Se2-xSx are found in experiments to possess spin spiral structures for x = {0-1.5} and at a concentration x = 1.75 the alloys become ferromagnetic. As S takes the place of Se in the crystal structure the distance between the Co layers is reduced and the turn angle of the spin spiral becomes smaller until it totally vanishes at x = 1.75. This thesis show that the evolution of the magnetic structure in these alloys is the consequence of a modification of the distance between Co layers, which induces a change in the interlayer exchange coupling. Fermi surfaces have been analyzed in TbNi5 in order to determine nesting features which would be responsible for the magnetic spin spiral observed in this material. The electronic structure of CeRhIn5 is also reported in this thesis. Furthermore, the 3-k magnetic structure of UO2 was investigated and the crystal field levels were calculated. Transition metal systems such as Fe in the superconducting high-pressure hcp phase and in the fcc crystal structure were also studied. The results obtained for fcc Fe are in accordance with previous reports. However the paramagnetic state in hcp Fe is found to be more stable than the antiferromagnetic configurations discussed earlier in the literature as being favored in the volume range where the hcp phase is stable and superconductivity appears (~ 15 GPa). The complex non-collinear magnetic structure in Mn3IrSi was calculated and the results are found to be in good agreement with experiments.