This paper presents first-principles calculations of quasiparticle energies and band gaps of graphene nanoribbons (GNRs) using a many-electron Green's function approach within the GW approximation. The study focuses on armchair (AGNR) and zigzag (ZGNR) GNRs, which are quasi-one-dimensional structures with widths ranging from 0.4 to 2.4 nm. The results show that electron-electron interactions significantly influence the quasiparticle band gaps, with self-energy corrections ranging from 0.5 to 3.0 eV. These corrections are much larger than those found in bulk graphite or diamond, indicating that the quasi-one-dimensional nature of GNRs enhances the screening of Coulomb interactions. The quasiparticle band gaps of AGNRs and ZGNRs are found to depend on the width of the ribbons, with a size dependence that can be described by a formula involving an effective width correction. The results show that the band gaps of ZGNRs are influenced by spin polarization, which changes the screening type from that of a metal to that of a semiconductor. The self-energy corrections to the band gaps are significant for both AGNRs and ZGNRs, with the corrections being larger for ZGNRs due to the spin interaction. The study also shows that the electronic structure of ZGNRs has two notable characteristics: the top of the valence band and the bottom of the conduction band are composed mainly of edge states, and the spin interaction introduces a finite band gap. The self-energy corrections to the band gaps in ZGNRs are similar to those in AGNRs, with corrections ranging from 0.8 to 1.5 eV. The results suggest that GNRs may be viable for use in electronic devices due to their relatively large band gaps. The paper also discusses the implications of the results for future research and applications, noting that the enhanced self-energy correction in GNRs is due to their quasi-one-dimensional geometry and weakened screening. The study concludes that the calculated quasiparticle band gaps are within the most interesting range for potential applications in nanoelectronics.This paper presents first-principles calculations of quasiparticle energies and band gaps of graphene nanoribbons (GNRs) using a many-electron Green's function approach within the GW approximation. The study focuses on armchair (AGNR) and zigzag (ZGNR) GNRs, which are quasi-one-dimensional structures with widths ranging from 0.4 to 2.4 nm. The results show that electron-electron interactions significantly influence the quasiparticle band gaps, with self-energy corrections ranging from 0.5 to 3.0 eV. These corrections are much larger than those found in bulk graphite or diamond, indicating that the quasi-one-dimensional nature of GNRs enhances the screening of Coulomb interactions. The quasiparticle band gaps of AGNRs and ZGNRs are found to depend on the width of the ribbons, with a size dependence that can be described by a formula involving an effective width correction. The results show that the band gaps of ZGNRs are influenced by spin polarization, which changes the screening type from that of a metal to that of a semiconductor. The self-energy corrections to the band gaps are significant for both AGNRs and ZGNRs, with the corrections being larger for ZGNRs due to the spin interaction. The study also shows that the electronic structure of ZGNRs has two notable characteristics: the top of the valence band and the bottom of the conduction band are composed mainly of edge states, and the spin interaction introduces a finite band gap. The self-energy corrections to the band gaps in ZGNRs are similar to those in AGNRs, with corrections ranging from 0.8 to 1.5 eV. The results suggest that GNRs may be viable for use in electronic devices due to their relatively large band gaps. The paper also discusses the implications of the results for future research and applications, noting that the enhanced self-energy correction in GNRs is due to their quasi-one-dimensional geometry and weakened screening. The study concludes that the calculated quasiparticle band gaps are within the most interesting range for potential applications in nanoelectronics.