FT Pulsed ESR/Electron Spin Transient Nutation(ESTN) Spectroscopy has been, for the first time, extended to amorphous and powder states of materials. Recently, organic high-spin polymers and clusters have emerged. With the increasing molecular spin quantum number S and molecular weight of the polymers, cw ESR spectroscopy manifests its inherent disadvantages in discriminating high spins from S=1/2 and in determining the S’s for the complex mixture of various spin assemblages. An electron spin transient nutation (ESTN) method based on pulsed ESR spectroscopy has been for the first time applied to a quasi 1D neutral high-spin polymers (A) as one of the most complex amorphous spin assemblages, identifying that the first neutral high-spin polymer A is comprised of high-spin assemblages characterized by the even S’s greater than 1/2. The molecular quantum spin number S have been identified up to S=4, showing direct evidence of the occurrence of a high-spin polymer with a pi-topologically controlled spin polarization. Eelectron spin transient nutation spectroscopy is facile and useful method for the exclusive identification of S and ESR transitions even for the cases of apparently vanishing fine-structure splittings and for spin systems with residual fine-structure terms in the spin Hamiltonian Fundamental bases for the transient nutation method are described, emphasizing inherent advantages in the nutation spectroscopy from the methodological viewpoint. The salient feature of multiple-quantum nutations have been disclosed in this work.