abstract: In this dissertation, I present the results from my recent investigations into the interactions involving topological defects, such as magnetic monopoles and strings, that may have been produced in the early universe. I performed numerical studies on the interactions of twisted monopole-antimonopole pairs in the 't Hooft-Polyakov model for a range of values of the scalar to vector mass ratio. Sphaleron solution predicted by Taubes was recovered, and I mapped out its energy and size as functions of parameters. I also looked into the production, and decay modes of $U(1)$ gauge and global strings. I demonstrated that strings can be produced upon evolution of gauge wavepackets defined within a certain region of parameter space. The numerical exploration of the decay modes of cosmic string loops led to the conclusions that string loops emit particle radiation primarily due to kink collisions, and that their decay time due to these losses is proportional to $L^p$, where $L$ is the loop length and $p \approx 2$. In contrast, the decay time due to gravitational radiation scales in proportion to $L$, and I concluded that particle emission is the primary energy loss mechanism for loops smaller than a critical length scale, while gravitational losses dominate for larger loops. In addition, I analyzed the decay of cosmic global string loops due to radiation of Goldstone bosons and massive scalar ($\chi$) particles. The length of loops I studied ranges from 200-1000 times the width of the string core. I found that the lifetime of a loop is approximately $1.4L$. The energy spectrum of Goldstone boson radiation has a $k^{-1}$ fall off, where $k$ is the wavenumber, and a sharp peak at $k\approx m_\chi/2$, where $m_\chi$ is the mass of $\chi$. The latter is a new feature and implies a peak at high energies (MeV-GeV) in the cosmological distribution of QCD axions. / Dissertation/Thesis / Doctoral Dissertation Physics 2020