This paper presents a two-dimensional model for mesons, developed by G. 't Hooft. The model is based on a gauge theory for strong interactions, where planar diagrams dominate. In one space and one time dimension, these diagrams can be reduced to self-energy and ladder diagrams, which can be summed. The gauge field interactions resemble those of a quantized dual string, and the physical mass spectrum forms a nearly straight "Regge trajectory". The model uses a local gauge group $ U(N) $, with $ N $ being large, allowing a perturbation expansion with respect to $ 1/N $. The Lagrangian includes terms for the gauge fields and quarks, with specific definitions for the fields and their interactions. The model is analyzed in light cone coordinates, with the light cone gauge condition $ A_{-} = A^{+} = 0 $, simplifying the equations. The model's Feynman rules are given, and the algebra for the $ \gamma $ matrices is defined. The self-energy parts of the quark propagator are analyzed, leading to a bootstrap equation for the self-energy. The model is then considered in the limit $ N \to \infty $, with only planar diagrams and no Fermion loops. The resulting propagator is analyzed, showing an infra-red divergence, leading to a shift in the pole of the propagator. The ladder diagrams satisfy a Bethe-Salpeter equation, and the spectrum of two-particle states is analyzed. The model is shown to have a straight "Regge trajectory" with no continuum corresponding to a state with two free quarks. The eigenvalues of the Hamiltonian are analyzed, showing a straight line for the mass spectrum, with no continuum. The model is compared to two-dimensional massless quantum electrodynamics, showing differences in the spectrum and the nature of the interactions. The paper concludes that the model provides a simple yet effective description of strong interactions, with a nearly straight Regge trajectory and no continuum. The results are validated through numerical calculations and comparisons with known results. The model is found to have limitations, such as the absence of transverse motions and the lack of particles like photons. The paper also discusses the need for further study of the unitarity condition for finite $ N $.This paper presents a two-dimensional model for mesons, developed by G. 't Hooft. The model is based on a gauge theory for strong interactions, where planar diagrams dominate. In one space and one time dimension, these diagrams can be reduced to self-energy and ladder diagrams, which can be summed. The gauge field interactions resemble those of a quantized dual string, and the physical mass spectrum forms a nearly straight "Regge trajectory". The model uses a local gauge group $ U(N) $, with $ N $ being large, allowing a perturbation expansion with respect to $ 1/N $. The Lagrangian includes terms for the gauge fields and quarks, with specific definitions for the fields and their interactions. The model is analyzed in light cone coordinates, with the light cone gauge condition $ A_{-} = A^{+} = 0 $, simplifying the equations. The model's Feynman rules are given, and the algebra for the $ \gamma $ matrices is defined. The self-energy parts of the quark propagator are analyzed, leading to a bootstrap equation for the self-energy. The model is then considered in the limit $ N \to \infty $, with only planar diagrams and no Fermion loops. The resulting propagator is analyzed, showing an infra-red divergence, leading to a shift in the pole of the propagator. The ladder diagrams satisfy a Bethe-Salpeter equation, and the spectrum of two-particle states is analyzed. The model is shown to have a straight "Regge trajectory" with no continuum corresponding to a state with two free quarks. The eigenvalues of the Hamiltonian are analyzed, showing a straight line for the mass spectrum, with no continuum. The model is compared to two-dimensional massless quantum electrodynamics, showing differences in the spectrum and the nature of the interactions. The paper concludes that the model provides a simple yet effective description of strong interactions, with a nearly straight Regge trajectory and no continuum. The results are validated through numerical calculations and comparisons with known results. The model is found to have limitations, such as the absence of transverse motions and the lack of particles like photons. The paper also discusses the need for further study of the unitarity condition for finite $ N $.