Molecular magnets with different dimensionality, whether they are zero-dimensional singlemolecule magnets (SMM) or one-dimensional single-chain magnets (SCM) are very interesting, since they allow probing the fundamental aspects bordering quantum and classical physics at the nanoscale level. This dissertation covers experimental studies of two Mn-based exchangecoupled molecule-based magnets and two Co-based single-chain magnets, using both dc Halleffect magnetometry and electron paramagnet resonance (EPR) techniques. In these multidimensional systems, the spin of the molecule exhibits quantum mechanical behavior at low temperature. It is quite interesting to observe the effect of magnetic exchange interactions on the magnetic properties of various complexes; hence they strongly affect the magnetic behavior. In this dissertation, the research is initiated with the study of low-magnetic-nuclearity molecules, starting with a spectroscopic study of a significantly anisotropic Mn(IV) monomer. At low temperature the molecule possesses easy-plane type anisotropy of a remarkable magnitude. Although the molecule is not a single-molecule magnet, the remarkable anisotropy can initiate synthesis of newer and better molecular magnets with Mn(IV) as the main building block. Furthermore, the interplay between the magnetic anisotropy and the inter-ion exchange interactions (J) within the molecule are probed for a dimer and a trimer where the magnetic core is comprised of two and three ions respectively. In the Mn-based case of the dimer, the low coupling between the atoms leads to significant state mixing, thus making it impossible to assign the individual spin states to the dimer or to the respective individual Mn(II) ions. In the case of iv the trimer, lowering of the symmetry achieved by fine tuning of the inter-ion exchange interactions leads to relieving of frustration in the antiferromagnetic (AF) triangular Mn(III) system, resulting in a well defined ground state and significant zero field splitting. Also a clear hysteretic behavior observed in this system demonstrates its SMM nature at low temperature. Finally, high-field high-frequency magnetic and spectroscopic studies performed on two cobalt-based SCMs reveal that formation of magnetic domains by exchange interactions within the chain are strongly influenced by thermal fluctuations. The chain possesses a uniaxial anisotropy with the quantization axis lying along the length of the chain. Moreover it is shown that modulation of the magnitude of inter- and intra-chain interactions results in a threedimensional dynamics in one of the samples. Interestingly, detailed dc magnetic studies show a tunable crossover between one- and three-dimensional magnetic dynamics as a function of temperature and/or magnetic field sweep rate. Our voyage through several molecular systems of different dimensionality have allowed us to expand our understanding of the role of exchange interactions on the magnetic behavior in molecular magnetism