28Si is formed by successive alpha captures on 12C during the AGB (asymptotic giant branch) stage of stellar burning. The last reaction in this series, 24Mg(alpha,gamma)28Si, has not been examined with sufficient sensitivity at alpha energies below 1.5 MeV. Several 28Si states appear favorable for formation by this reaction in the alpha energy range of 1.0 - 1.5 MeV, motivating a new study of this reaction at the University of Notre Dame. To maximize experimental sensitivity, a high efficiency coincidence detection system was developed. Several previously unknown resonances were observed between 1.1 and 1.5 MeV, and an upper limit for any lower energy resonances was obtained. Resonance parameters were determined and reaction rates were calculated. Additionally, neutron capture reactions on the stable magnesium isotopes were studied at the n_TOF facility. The data were fit using the R-matrix code SAMMY; newly calculated resonance parameters are presented.