"Nonlinear field theories, which possess soliton solutions as part of their energy spectrum, are of great interest in mathematical physics. A soliton is a finite-energy solution of a nonlinear partial differential equation, which is stabilized by a conserved charge associated with the field theory. The analysis of solitons necessitates a large expanse of mathematical techniques, often merging analytical and geometrical techniques with sophisticated numerical ones. Advancements in computing power have meant many more soliton solutions can be obtained numerically. This has made much more intricate and computationally intensive soliton simulations possible, making solitons a very interesting modern topic. The theory of solitons is particularly appealing since not only are interesting mathematical structures but also appear in cosmology, nuclear and high energy physics, condensed matter and even in nano-technology. Moreover, in the effort of creating soliton solutions significant advancements have been made in numerical analysis, symbolic computer algebra and differential geometry.The ambitious aim of this project is to provide a link between fundamental theory, particle physics and cosmology through a novel mathematical description, using geometrical formulation, in which particles arise as stable localized excitations corresponding to topological solitons."