The chemical and physical processes underlying the formation of soot during combustion have been numerically studied using fundamental combustion chemistry and aerosol dynamics theory. A detailed gaseous phase reaction mechanism, which describes the formation and growth of soot precursors including PAH and polyynes, and soot chemistry, which includes the particle nucleation, heterogeneous surface growth, and PAH surface condensation, were coupled to an advanced sectional aerosol dynamics model which is able to calculate the coagulation process of soot agglomerates with fractal structures in three Knudson number regimes. Three studies have been carried out to predict major soot forming characteristics such as particle yield, total number density, averaged particle diameter, and particle size distribution. The first study focused on the investigation of surface growth and condensation processes related to the formation of soot in a Jet Stirred Reactor and Plug Flow Reactor system. The second study looked at the nucleation and surface growth processes during the early stages of soot formation. The third and final study involved modeling the formation of carbonaceous nanoparticles during the thermal decomposition of hydrogen free carbon bearing molecules, such as C₃O₂ and CCl₄. behind shock waves. The chemical kinetics concerning pure carbon clusters and particulate coagulation were studied for soot particle formation in the absence of the HACA surface growth mechanism. The numerical simulations showed that the sectional aerosol dynamics models developed in this study were able to be coupled with complex physical processes, such as thermal re-structuring, carbonization, and agglomerate coagulation. Studying the soot formation in a JSR/PFR system revealed that both the HACA surface growth mechanism and the PAH condensation process play significant roles in the growth of soot mass at larger residence times. The investigation of soot formation during the pyrolysis of C₆H₆ behind a shock wave demonstrated that both the PAH growth pathway and the fast polyyne polymerization process contribute to the early formation of soot particles. Finally, the simulation results of the pyrolysis of C₃O₂ behind a shock wave were in good agreement with measured characteristics of nanoparticle yield.