In this thesis we investigated structural, electronic and magnetic properties of 3d (light) transition metal (TM) atomic chains and Cr nanowires using firstprinciples pseudopotential plane wave calculations. Infinite periodic linear, dimerized linear and planar zigzag chain structures, as well as their short segments consisting of finite number of atoms and chromium nanowires have been considered. For most of the infinite periodic chains, neither linear nor dimerized linear structures are favored; to lower their energy the chains undergo a structural transformation to form planar zigzag and dimerized zigzag geometries. Dimerization in both infinite and finite chains are much stronger than the usual Peierls distortion and appear to depend on the number of 3d-electrons. As a result of dimerization, a significant energy lowering occurs which, in turn, influences the stability and physical properties. Metallic linear chain of vanadium becomes half-metallic upon dimerization. Infinite linear chain of scandium also becomes half-metallic upon transformation to the zigzag structure. The end effects influence the geometry, energetics and the magnetic ground state of the finite chains. Structure optimization performed using noncollinear approximation indicates significant differences from the collinear approximation. Variation of the cohesive energy of infinite and finite-size chains with respect to the number of 3d-electrons are found to mimic the bulk behavior pointed out by Friedel. Furthermore, we considered Cr nanowires, which have cross section comprising a few (4,5 - 9,12) atoms. Chromium nanowires are found to be in a local minimum in the Born-Oppenheimer surface and are ferrimagnetic metals. The type of coupling, as for ferromagnetic or antiferromagnetic, between neighboring Cr atoms depends on their interatomic distances. The spin-orbit coupling of finite chains are found to be negligibly small for finite molecules and Cr nanowires.