The paper discusses the properties of spinor Bose condensates in optical traps, focusing on the ground state structures and collective modes of spin-1 Bosons such as ${}^{23}$Na, ${}^{39}$K, and ${}^{87}$Rb. The ground state can be either ferromagnetic or polar, depending on the scattering lengths in different angular momentum channels. The ferromagnetic state exhibits coreless (or Skyrmion) vortices, similar to those in superfluid ${}^{3}$He-A, while the polar state has stable vortices with unit circulation. The paper also derives the effective low-energy Hamiltonian for these systems, which is crucial for understanding their behavior. The Hamiltonian is derived for Bosons with hyperfine spin $f = 1$ and is shown to depend on the s-wave scattering lengths $\{a_F\}$ of various elastic scattering channels. The paper further explores the collective modes of these condensates, including density modes and spin wave modes, and discusses the intrinsic stability of singular vortices with circulation $(\ell>1)$ in the ferromagnetic state. The results highlight the unique quantum phenomena absent in scalar condensates, such as the existence of coreless vortices and the topological and energetic instability of doubly quantized singular vortices.The paper discusses the properties of spinor Bose condensates in optical traps, focusing on the ground state structures and collective modes of spin-1 Bosons such as ${}^{23}$Na, ${}^{39}$K, and ${}^{87}$Rb. The ground state can be either ferromagnetic or polar, depending on the scattering lengths in different angular momentum channels. The ferromagnetic state exhibits coreless (or Skyrmion) vortices, similar to those in superfluid ${}^{3}$He-A, while the polar state has stable vortices with unit circulation. The paper also derives the effective low-energy Hamiltonian for these systems, which is crucial for understanding their behavior. The Hamiltonian is derived for Bosons with hyperfine spin $f = 1$ and is shown to depend on the s-wave scattering lengths $\{a_F\}$ of various elastic scattering channels. The paper further explores the collective modes of these condensates, including density modes and spin wave modes, and discusses the intrinsic stability of singular vortices with circulation $(\ell>1)$ in the ferromagnetic state. The results highlight the unique quantum phenomena absent in scalar condensates, such as the existence of coreless vortices and the topological and energetic instability of doubly quantized singular vortices.