Liquid chromatography is a separation and purification process that has attracted attention due to its wide usage in biological, biochemical, fine chemicals, pharmaceutical and food processing industries. The task of this dissertation is focused on the theoretical study of linear and nonlinear liquid chromatographic processes in thermally insulated cylindrical columns packed with either fully-porous or core-shell particles and operating under either isothermal or non-isothermal conditions. Both non-reactive and reactive chromatographic processes are analyzed. In the latter case, separation and conversion of the reactants into products takes place concurrently. A two-dimensional general rate model (2D-GRM) in cylindrical coordinates is formulated to simulate these processes. For the simulation of linear chromatography, the finite Hankel and the Laplace transformations are applied one after another to obtain analytical solutions of the linear model equations for two different sets of boundary conditions. To further elaborate the process, the analytical temporal moments are obtained from the Hankel-Laplace domain solutions. These moments are very useful for analyzing the retention times, band broadenings and front asymmetries of elution profiles. The derived analytical solutions and moments are very useful for diluted or small volume samples. However, to simulate chromatographic process for concentrated or large volume samples, the numerical approximations of nonlinear model equations are needed. In this thesis project, a high-resolution finite volume scheme (HR-FVS) is extended and applied to solve the resulting 2D-model equations in cylindrical coordinates. Several case studies are conducted for a wide range of thermodynamic, kinetic and reaction coefficients. Furthermore, the coupling between concentration fronts and thermal waves are demonstrated through graphs and essential parameters influencing the column (or reactor) performance are pinpointed. A few consistency tests are also conducted for assessing the process performance. The solutions obtained are useful tools for analyzing, optimizing and upgrading the liquid chromatographic processes.