Bose-Einstein condensation of dilute ultracold alkali atom gases was achieved in 1995, and since then, these highly controllable macroscopic quantum systems have attracted wide interest. The dilute condensates provide a rare opportunity to model interacting many-body systems exhaustively and accurately from first- principles quantum field theories. One of the main signatures of Bose-Einstein condensation is superfluidity: particle currents can flow without dissipation and viscosity. The superfluidity of the condensates is intimately related to the existence and stability of topological phase singularities called quantized vortices. The trapped alkali atom gases can be either spin-polarized, or they may support different coexisting spin orientations. In this Master's Thesis, we investigate multiply quantized vortices in both scalar and spinor condensates in the zero-temperature limit. We study computationally the core size and dynamic instability of multiquantum vortices in axisymmetric scalar condensates. We also investigate the splitting mechanisms of such vortices into singly quantized ones. Furthermore, we study topological phase imprinting methods that can be used to create multiply quantized vortices in spinor condensates. Our numerical studies showed that the dynamic instability of a multiply quantized vortex increases only slightly as a function of the quantum number. It was found that the splitting of multiquantum vortices results in the formation of vortex sheets and large vortex-free domains in the condensates. We also demonstrated that vortices with odd quantum numbers can be topologically created in spinor condensates through a cyclic control of external magnetic fields.