The muon's magnetic moment is associated with its spin through the gyromagnetic factor g. In the Standard Model (SM) framework, predicting the g-factor requires considering higher-order effects, such as the perturbative calculation of the single-loop quantum electrodynamic (QED) contribution involving the exchange of virtual photons and fermion pairs. This contribution, known as the Schwinger term, leads to a radiative correction of the g-factor at the scale of the fine-structure constant. Moreover, all SM sectors contribute to radiative correction. For example, muon can couple to the hadronic vacuum polarization through virtual photons as a result of quantum mechanical fluctuations. Therefore, measuring the anomalous magnetic moment of muon a_mu allows for testing the SM and probing hypothetical new particles predicted by physics beyond the SM (BSM). Due to the muon’s heavy mass, a_mu is particularly sensitive to BSM physics. Currently, the experimental value of a_mu shows a discrepancy of approximately 4.2 sigma compared to the SM prediction. The latest result from the g-2 experiment at Fermilab has increased the present accuracy by a factor of four. On the other hand, new experimental results are being incorporated into the ongoing theoretical calculations, and it is expected to shift the central value of the predicted a_mu, potentially revealing the discrepancy at a new level. The primary source of uncertainty in the theoretical evaluation of a_mu arises from the hadronic vacuum polarization contribution at the leading order. Accurate measurements of the hadronic R-ratio and therefore of the total cross sections of various hadronic states produced in e+e− annihilation are required for its evaluation using dispersive relations. The e+e− → pi+pi− (gamma) channel brings about 75% of the hadronic contribution and 43% of the total uncertainty squared to a_mu. The measurement of the 2pi channel has been pioneered at KLOE/KLOE-2 (Laboratori Nazionali di Frascati (LNF) near Rome in Italy.) using the initial state radiation (ISR) technique, and subsequent measurements have been performed at BaBar and BESIII, providing comprehensive and significant data sets for the cross section sigma_{2pi} . The second largest contribution, accounting for about ∼ 4.6%, comes from the 3pi channel. The cross section sigma_{3pi} is dominated by vector meson resonances, such as omega, phi and J/psi. In the lower center-of-mass (c.m.) energy region up to the phi mass, sigma_{3pi} has been measured using conventional energy scans, for example at SND and CMD-2, where the vector-meson parameters and line shape are accurately determined. In this project, the ISR technique is employed to provide a visible cross section sigma_{3pi} data set below 1 GeV at KLOE/KLOE-2. The ISR process e+e− → gamma^{∗}gamma → pi+pi−pi0gamma is studied using a data sample of 1.7 fb−1 collected during the period 2004-2005. The cross section sigma_{3pi} is determined in the c.m. energy range between 760 and 800 MeV/c^{2}. From the 3pi invariant mass spectrum, the peak cross section of the omega-meson resonance, its mass m_{omega} , width Γ_{omega} , and the product branching fraction B (omega → e+e−) × B (omega → 3pi) are extracted.