The MgB2 superconductor has significant potential for practical applications. The main points of strength are its critical temperature close to 40 K, which may allow operating in cryogen-free environments, the low cost of precursor materials, and the ease of manufacture. However, a large gap is present between the upper-critical-field, Bc2, values measured in MgB2 polycrystalline bulk superconductors and those of thin films, where values as high as ≳ 50 T have been achieved at 4.2 K. Filling this gap would unlock the potential of MgB2 for magnet applications. This thesis presents a systematic study of the effects of the synthesis conditions on Bc2 of binary and C-doped bulk samples. Guided by the Design of Experiment (DoE) statistical approach, we employed a novel rapid-synthesis route and successfully identified a broad region of the synthesis parameters that maximizes Bc2 up to record-high values.