The chemical shift and spin-spin coupling constant are two most important phenomena observed and analysed by NMR techniques, giving information about the chemical and physical aspects of the electronic structure of molecules. In this thesis we present an investigation from two different viewpoints of the above NMR parameters. Chapter I gives a general introduction to the field of NMR, which is required for the theoretical interpretation and understanding of the chemical shift and spin-spin coupling constant. In Chapter 2 an empirical approach is taken for the calculation of electronic wave functions used in evaluating the chemical shifts of carbon, nitroqen, and oxygen nuclei in a wide range of compounds. In this method a set of parameters for calculating molecular wave functions within the HUckel approximation were obtained by minimisation of the differences between observed and calculated chemical shifts of the nuclei in a few selected compounds. The simplicity of this method makes it possible to apply it to molecules of some complexity. The second part of the thesis, Chapter 3, gives a detailed analysis of the basic assumptions commonly made in calculating spin-spin coupling constants. The Fermicontact term, which is the main contributor to indirect spin-spin coupling interactions, is derived and discussed. We have shown how the hyperfine interaction Hamiltonian (containing the Fermi-contact term) is obtained from Dirac's electron theory. The usual 6(r) representation of the Fermi-contact term is shown to be inconsistent, as it leads to an infinite second order perturbation correction to the energy of the hydrogenic ground state. In order to overcome this inconsistency the finite size nucleus model was proposed, leading to a new representation of the Fermi-contact term. To obtain a wave function adequate for the description of this perturbation, the variation-perturbation approach was found suitable. This method requires only the minimisation with respect to one parameter of the trial wave function for the chosen form of the Hamiltonian. Using this procedure calculations were made of the hyperfine splitting of the hydrogenic ground state, and the results are tabulated and discussed. This work clearly indicates the inadequacy of using the 6(r) function in the Fermi-contact term, a term of . great importance for the calculation of spin-spin coupling constants in molecules.