Glutamate, glutamine, and gamma-Aminobutyric acid play important excitatory and inhibitory messenger role in neuronal signal transmissions. Perturbations in the delicate homeostatic balances between these three neurometabolites have significant implications in various psychiatric disorders. Proton magnetic resonance spectroscopy is a non-invasive analytical technique that allows the detection and quantification of in vivo chemical compound concentrations under the image guidance of MRI. A variety of MRS acquisition methods have been employed in the past to study the GABAergic and glutamatergic systems in the human brains, sometimes with conflicting reports in the metabolite levels. The variability in findings is likely caused by the methodology differences in acquisition and quantification steps of these studies. In this thesis, I performed quantum mechanical based numerical simulations to investigate how the LCModel quantification accuracy varies with different acquisition parameters and baseline signals. The simulation results show that Gln cannot be reliably measured at 1.5 T and 3 T with the PRESS acquisition and the Spin Echo method. Glu can be reliably measured at 1.5 T, 3 T, and 7 T with both the PRESS and Spin Echo method. I also applied the MEGA-PRESS pulse sequence to measure GABA concentrations in both phantoms and healthy human controls. Two MRS quantification methods were used to quantify the C4 GABA resonances with the edited spectra. The results show that both the LCModel and peak integration techniques offer similar inter-subject CV in GABA signal quantifications. I also present a novel post-processing technique called the Fast Pade Transform to investigate its feasibility and accuracy as an alternative method to measure glutamate, glutamine, and GABA in human brains. The results show that the FPT algorithm is capable of quantifying resonance peaks of GABA, tNAA, tCr, and tCho with good agreement to the LCModel method, but there is no indication that FPT produces more accurate or precise concentrations. Performance of the FPT algorithm for Glu and Gln quantification is inferior to LCModel quantification.