Double spin asymmetries for the proton and the deuteron have been measured in the EG1b experiment using the CLAS detector at Jefferson Lab. Longitudinally polarized electrons at energies 1.6, 2.5, 4.2 and 5.7 GeV were scattered from longitudinally polarized NH₃ and ND₃ targets. The double spin asymmetry A_|| for the proton and the deuteron has been extracted from these data as a function of W and Q ² with unprecedented precision. The virtual photon asymmetry A₁ and the spin structure function g ₁ can be calculated from these measurements by using parametrization to the world data for the virtual photon asymmetry A ₂ and the unpolarized structure functions F₁ and R. The large kinematic coverage of the experiment (0.05 GeV² < Q² < 5.0 GeV² and 1.08 GeV < W < 3.0 GeV) helps us to better understand the spin structure of the nucleon, especially in the transition region between hadronic and quark-gluon degrees of freedom. The results on A₁, g₁ and the first moment [special characters omitted], as well as the higher moments [special characters omitted] and [special characters omitted], using the entire data set for the deuteron, are presented in this thesis. The moments are compared to theoretical and phenomenological calculations. In addition, parameterizations of the world data on the asymmetries and the spin structure functions are studied to create and refine the models on these quantities that can be used in various applications. Finally, the neutron asymmetries are extracted from the combined proton and deuteron data and the preliminary results are demonstrated.