Nuclear magnetic resonance (NMR) is an important phenomenon involving nuclear magnetic moments in magnetic field, which can provide much information about a wide range of materials, including their chemical composition, chemical environments and nuclear spin interactions. The NMR spectrometer has been extensively developed and used in many areas of research. In this thesis, studies in two different areas using NMR are presented. First, a new kind of nanoparticle, Gd(DTPA) intercalated layered double hydroxide (LDH), has been successfully synthesized in the laboratory of Prof. Dey in SEMTE at ASU. In Chapter II, the NMR relaxation studies of two types of LDH (Mg, Al-LDH and Zn, Al-LDH) are presented and the results show that when they are intercalated with Gd(DTPA) they have a higher relaxivity than current commercial magnetic resonance imaging (MRI) contrast agents, such as DTPA in water solution. So this material may be useful as an MRI contrast agent. Several conditions were examined, such as nanoparticle size, pH and intercalation percentage, to determine the optimal relaxivity of this nanoparticle. Further NMR studies and simulations were conducted to provide an explanation for the high relaxivity. Second, fly ash is a kind of cementitious material, which has been of great interest because, when activated by an alkaline solution, it exhibits the capability for replacing ordinary Portland cement as a concrete binder. However, the reaction of activated fly ash is not fully understood. In chapter III, pore structure and NMR studies of activated fly ash using different activators, including NaOH and KOH (4M and 8M) and Na/K silicate, are presented. The pore structure, degree of order and proportion of different components in the reaction product were obtained, which reveal much about the reaction and makeup of the final product.