The MuSun experiment will determine the μd capture rate (μ−+d ->n+n+νe) from the doublet hyperfine state Λd, of the muonic deuterium atom in the 1S ground state to a precision of 1.5%. Modern effective field theories (EFT) predict that an accurate measurement of Λd would determine the two-nucleon weak axial current. This will help in understanding all weak nuclear interactions such as the stellar thermonuclear proton-proton fusion reactions, the neutrino reaction ν+d (which explores the solar neutrino oscillation problem). It will also help us understand weak nuclear interactions involving more than two nucleons — double β decay — as they do involve a two-nucleon weak axial current term. The experiment took place in the πE3 beam-line of Paul Scherrer Institute (PSI) using a muon beam generated from 2.2 mA proton beam — which is the highest intensity beam in the world. The muons first passed through entrance scintillator and multiwire proportional chamber for determining thier entrance timing and position respectively. Then they were stopped in a cryogenic time projection chamber (cryo- TPC) filled with D2 gas. This was surrounded by plastic scintillators and multiwire proportional chambers for detecting the decay electrons and an array of eight liquid scintillators for detecting neutrons. Muons in deuterium get captured to form μd atoms in the quartet and doublet spin states. These atoms undergo nuclear capture from these hyperfine states respectively. There is a hyperfine transition rate from quartet-to-doublet state — λqd along with dμd molecular formation which further undergoes a fusion reaction with the muon acting as a catalyst (MCF). The goal of this dissertation is to measure the dμd quartet-to-doublet rate ratio (λq : λd) and μd hyperfine rate (λqd) using the fusion neutrons from μ− stops in D2 gas. The dμd molecules undergo MCF reactions from the doublet and the quartet state with rates λq and λd and yield 2.45 MeV monoenergetic fusion neutrons. Encoded in the time dependence of the fusion neutrons are the dμd formation rates λq, λd and hyperfine rate λqd . Consequently, the investigation of the fusion neutron time spectrum enables the determination of these kinetics parameters that are important in the extraction of Λd from the decay electron time spectrum. The final results of this work yield λq : λd = 85.51 ± 3.25 and λqd = 38.49 ± 0.21 μs−1.