We report a systematic investigation of the local electronic, magnetic, and superconducting properties of the new iron-based high temperature superconductor Ba(Fe(1-x)Co(x)As(2) (x = 0, 0.02 , 0.04, 0.082) through the measurement of 75As and 59Co NMR (Nuclear Magnetic Resonance) lineshapes, Knight shift (K), and spinlattice relaxation rate ( 1/ T1) . The 75As NMR lineshape of the undoped parent compound splits into two sets due to discrete values of hyperfine magnetic field B(c)(hf)= ±1.32 Tesla below the magnetic ordering temperature to the SDW (Spin Density Wave) state, TSDW. In contrast, for lightly Co doped samples with x=0.02 and 0.04, the 75As and 59Co lineshapes become broad and featureless below Tsnw , indicating that the ground state is no longer the commensurate SDW ordered state. The observed lineshape is consistent with an incommensurate SDW ordered state, or a commensurate state with large distribution of hyperfine field Bhf. In the optimally doped superconductor with x = 0.082 (Tc = 22 K) , we observe two types of As sites and three types of Co sites, respectively, as expected from a binomial distribution of Co dopants. We found no evidence for induced localized moments in the vicinity of Co dopants. This finding is in remarkable contrast with the case of Zn or Ni doped high Tc cuprates, and suggests that the fundamental physics of iron-based superconductors is different from that of cu prates. The temperature dependences of 75,59K and 75,59 (1/T1T) at both 75As and 59Co sites show that Ba(Fe(1-x)Co(x))(2)As(2) exhibits spin pseudo-gap like behavior down to ~100 K for a broad Co concentration range. Below ~100 K , we observe the enhancement of residual antiferromagnetic spin fluctuations associated with inter-band spin excitations between the hole and electron Fermi surfaces even for x= 0.082. This effect is suppressed in the overdoped sample with x= 0.099, and Tc decreases. Therefore, we suggest that antiferromagnetic spin fluctuations play a crucial role in the superconducting mechanism of Ba(Fe(1-x)Co(x))(2)As(2) . We also demonstrate that the superconductivity arises from a novel electronic state with spin susceptibility Xs ~ constant and in-plane resistivity P(ab)~T, which is not consistent with canonical Fermi-liquid behavior. / Thesis / Doctor of Philosophy (PhD)