Soft condensed matter is the study of flexible materials that change their shape under the influence of a weak force. Typical examples are polymers and liquid crystals. Chromonic liquid crystals consist of molecules having a hydrophobic flat aromatic core to which have been attached ionic groups or non-ionic groups. These disk-like molecules self-assemble into ordered phases in the presence of solvents, aggregating in a face-to-face fashion, and creating stackedlinear molecular aggregates. The degree of self-organization into columns depends on the concentration, temperature, and pressure. Depending on the types of terminal groups, the molecules can be dissolved in organic solvents or water. A theoretical study was performed to model the detailed effects of adding stacking, translation, and rotation energy on the length distribution of chromonic liquid crystals. A second derivative test was done to prove that all the solutions for isotropic phases are at a global minimum of the free energy. The free energies and length distributions for various nematic phase formulations are presented. Free energy and length distribution for both Maier-Saupe and Onsager interactions are presented. The free energy and length distribution for considering I-N phase co-existence and no phase co-existence are presented. It is shown that the nematic phase solutions all lead to a first-order phase transition. The nematic phase solution with the Maier-Saupe interaction causes the averaged aggregate length to increase when the system transitions from the isotropic phase to the nematic phase, while the nematic phase solution with the Onsager interaction causes the averaged aggregate length to decrease.Another major component of this thesis is the study of glass transitions. An analytical study that aims to describe the mean squared displacement at low temperatures is presented. The short-time and long-time limit of the analytical solution are discussed. Then, an approach utilizing machine learning algorithms is developed for predicting the glass transition temperature of polystyrene (PS) and poly(methyl methacrylate) (PMMA) from short-time simulations. This approach predicts a 360K glass transition temperature for PS and 400K for PMMA.It is found that the biggest change in the average Non-Gaussian parameter happens (NGP) at the same temperature as the biggest change in variance of the Non-Gaussian parameter (NGP), namely 420K for PS and 460K for PMMA. The fact that the above temperatures are slightly higher than the glass transition temperatures predicted by our approach above, we hypothesize that the increase in the dynamic heterogeneity is a precursor to the glass transition.