Spinor Bose condensates in optical traps are studied, focusing on the ground state structures and collective modes of spin-1 bosons like $^{23}$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 polar state supports density and vector-like spin wave modes, while the ferromagnetic state has vector-like and quadrupolar-like spin wave modes. The ferromagnetic state also exhibits coreless (or Skyrmion) vortices similar to those in superfluid $^{3}$He-A. Optical traps allow the spin of alkali atoms to be free, enabling the study of spinor nature. The effective low energy Hamiltonian describes the interactions and spin dynamics. The ground state structure depends on the s-wave scattering lengths, with the polar state having $a_2 > a_0$ and the ferromagnetic state having $a_0 > a_2$. Collective modes in the polar state are of Stringari form, while those in the ferromagnetic state have different characteristics. Vortices in the ferromagnetic state are only topologically stable with unit circulation. The spinor nature of the condensate leads to unique quantum phenomena, including topological and energetic instabilities of higher circulation vortices and the existence of coreless vortices. The study highlights the differences in symmetry between polar and ferromagnetic states, leading to distinct vortex behaviors. The results are based on the effective Hamiltonian and the properties of the spinor condensates in optical traps.Spinor Bose condensates in optical traps are studied, focusing on the ground state structures and collective modes of spin-1 bosons like $^{23}$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 polar state supports density and vector-like spin wave modes, while the ferromagnetic state has vector-like and quadrupolar-like spin wave modes. The ferromagnetic state also exhibits coreless (or Skyrmion) vortices similar to those in superfluid $^{3}$He-A. Optical traps allow the spin of alkali atoms to be free, enabling the study of spinor nature. The effective low energy Hamiltonian describes the interactions and spin dynamics. The ground state structure depends on the s-wave scattering lengths, with the polar state having $a_2 > a_0$ and the ferromagnetic state having $a_0 > a_2$. Collective modes in the polar state are of Stringari form, while those in the ferromagnetic state have different characteristics. Vortices in the ferromagnetic state are only topologically stable with unit circulation. The spinor nature of the condensate leads to unique quantum phenomena, including topological and energetic instabilities of higher circulation vortices and the existence of coreless vortices. The study highlights the differences in symmetry between polar and ferromagnetic states, leading to distinct vortex behaviors. The results are based on the effective Hamiltonian and the properties of the spinor condensates in optical traps.