In this seminar we will discuss cosmology from the era of nucleosynthesis and recombination leading up to the era of reionization. We will begin with the success of the Cosmic Microwave Background (CMB) as a probe for the Lambda Cold Dark Matter cosmology model, and tests of inflation. Subsequently, we will discuss upcoming frontier physics of 21-cm neutral hydrogen emission that traces the evolution of the Universe, from the dark ages to the earliest star formation epochs. CMB discussions will focus on reconstruction of the inflationary primordial power spectrum (PPS) of the seed perturbations, and weak gravitational lensing of CMB photons, their effects, and attempts at their reconstruction. 21-cm discussions will examine current approaches aimed at detecting the faint radio line over the range of redshifts probing the dark ages and reionization of the universe. We will discuss the estimators and statistical models used to recover the PPS and weak lensing power spectrum in the context of high precision cosmology and parameter inference, along with our results. We will then demonstrate how similar mathematical formalisms are being utilized to calibrate and design the next generation of radio interferometers in the 21cm signal search, our preliminary results from observations through Hydrogen Epoch of Reionization Array (HERA) and overall prospects in high precision cosmology for the upcoming decades.