Four sol-gel systems (alumina, aluminum hydroxide, zirconia, and magnesia) were investigated, primarily by laser spectroscopy, on several series of materials prepared by systematically varying the synthesis procedures. Key material phases analyzed were: (1) nanocrystalline boehmite [AlO(OH)]; (2) bayerite, nordstrandite, and gibbsite [Al(OH)₃ polymorphs]; (3) amorphous zirconia [a-ZrO₂]; and (4) magnesite [MgCO₃], hydromagnesite [4MgCO₃·Mg(OH)₂·5H₂0], and magnesia [MgO]. Crystal nucleation and crystal growth kinetics were studied in several cases, with x-ray experiments carried out to calibrate the Raman-scattering technique I developed for monitoring crystallite size. Nanocrystalline boehmite, γ-AlO(OH), was found to be the principal component in the sol-gel alumina system. Materials were prepared by the hot-water hydrolysis/condensation of Al(OC₄H₉)₃, the Yoldas process, as a function of process variables such as the time spent in the sol phase. Small but systematic changes, as a function of sol aging time, were discovered in the lineshape and position of the dominant boehmite Raman band observed in the alumina hydrogels. These spectral changes were interpreted in terms of nanocrystallinity-induced finite-size effects associated with the slow growth of AlO(OH) nanocrystals in the sol. X-ray diffraction experiments were used to determine nanocrystal sizes (as small as 3 nm for gels prepared from fresh sols) and to estimate growth kinetics from the Raman-lineshape results. These results appear to be among the first available for crystallite growth kinetics (ripening) in the near-atomic-scale nanocrystal regime. The Raman peak-position shift is proportional to L^-α, where L is the average nanocrystal size and α is a Raman-versus-size scaling exponent. For AlO(OH), I determined α to be 1.0, close to the scaling-exponent values reported for graphite and BN and different from the values (about 1.5) that describe the reported behavior of Si, Ge, and GaAs. The trihydroxide polymorph system is closely related to the sol-gel alumina system. The processing temperature and the method of hydrolysis were varied, in order to determine their effect on the trihydroxide phase mix. The trihydroxide phase mix does not change with time; it depends only on the initial hydrolysis conditions. Bayerite is the primary phase present for materials processed at 25 C, while nordstrandite is the primary phase present for materials processed at 60 C. It is shown that the trihydroxide crystal nucleation kinetics are responsible for the Al(OH)₃ phase mix. Hydroxide/oxyhydroxide phase-mix kinetics were also studied; this ratio increases with time. The associated rate constant decreases with increasing temperature. Sol-gel zirconia was prepared by using atmospheric water to hydrolyze a mixture of zirconium propoxide, acetic acid, and n-propanol. This produces a clear gel. Hydrogen peroxide was found to chemically react with the gels. Clean Raman spectra reveal a broad-band structure (the full width at half maximum is 150 cm⁻¹) centered at about 460 cm⁻¹. This band is interpreted as the signature of an amorphous phase of zirconia. Raman and luminescent spectra (both obtained on the Raman spectrometer) were used to monitor the conversion of magnesium-carbonate-based materials to magnesium oxide, as a function of temperature. This new phase-determination technique utilizes the krypton 674.1 nm laser line so that the carbonate symmetric-stretch band and the MgO:Cr⁺⁺⁺ luminescence band are readily observable on the same spectrum. / Ph. D.