Run 2/3 measurement of the muon anomalous magnetic moment by the Muon g-2 experiment at Fermilab

The Muon g-2 experiment at Fermilab seeks to measure the muon magnetic moment anomaly, a_μ=(g-2)/2, with a final target precision of 0.14 parts-per-million (ppm). The experiment's initial result, published in 2021 using Run 1 data from 2018, confirmed the previous measurement at Brookhaven National Laboratory with a comparable sensitivity of 0.46 ppm. In 2023, a new result based on Run 2 and Run 3 data, collected in 2019 and 2020, was released. These datasets contain four times the data from Run 1, significantly enhancing sensitivity and achieving an unprecedented uncertainty of 0.20 ppm. This advancement resulted in a two-fold improvement in both statistical and systematic uncertainties. Here, we will discuss the muon $g-2$ measurement, the increased precision relative to the Run 1 result, and provide an outlook on future measurements which will incorporate datasets from 2021 to 2023. Additionally, we will explore the implications of comparing the new measurements with the latest Standard Model predictions for muon g-2.