The Neutron Star Interior Composition Explorer (NICER) is NASA's new X-ray timing instrument onboard the ISS that was launched in June 2017. With a large effective area, low background, very precise absolute timing and great low energy response, NICER has been doing a fantastic job in observing many interesting phenomena related to neutron stars and black holes. One of the main goals of the NICER mission is to constrain the equation of state of ultra-dense matter by measuring the masses and radii of several rotation-powered millisecond pulsars. This is being done by fitting pulse waveform models that incorporate all relevant relativistic effects and atmospheric radiation transfer processes to the periodic soft X-ray modulations produced by the rotation of hot spots located near the magnetic polar caps of these pulsars. Some of the other interesting topics that are being studied with NICER includes phenomena related to Type I X-ray bursts, which are thermonuclear flashes observed from the surfaces of accreting neutron stars in Low Mass X-ray Binaries, such as photospheric radius expansion and burst oscillations. NICER's large effective area and excellent low energy response enable new, detailed studies of these bursts in the soft X-ray band. In this talk I will present some of the early results from the first nine months of the NICER mission and will report on the progress being made by the NICER team in measuring the masses and radii of pulsars.