FAMU will realize the first measurement of the hyperfine splitting (hfs) in the 1S state of muonic hydrogen ΔEhfs(μ-p)1S - providing crucial information on proton structure and muon-nucleon interaction - by using an intense pulsed muon beam, and an on-purpose developed high-energy mid infrared tunable laser. FAMU initiates a new class of experiments representing a significant leap forward in the quality of spectroscopic measurements in muonic atoms; specifically, it will provide the proton Zemach radius rZ with higher precision than previously possible, disentangling discordant theoretical values and will quantify any level of discrepancy that may exist between values of rZ as extracted from normal and muonic hydrogen atoms. It will set a needed cornerstone result about not yet explained anomalies within the proton charge rch radius. The Zemach radius rZ and the r.m.s charge radius rch are the only proton shape-related values that can be directly extracted from experimental data, and rZ is the only one that carries information about the proton's magnetic dipole moment distribution. A pulsed intense muon beam entering the MUST hydrogen gas target will form muonic hydrogen atoms. FAMU's theoretical and experimental effort will establish new limits on the proton structure parameters measuring the muonic hydrogen transition ΔEhfs(μ-p)1S with unprecedented precision - δλ/λ < 10-5 - and will shed light on the low momentum limit of the magnetic-to-charge form factor ratio.