PhD (Physics), North-West University, Mafikeng Campus, 2015 In this thesis we study aspects of solar-like oscillations in the Sun and Red Giant stars. In the first part of the thesis, we re-calculate theoretical amplitude ratios and phase differences and compare with existing data in the Sun. Previous work to do the same was performed by Houdek ( 1996) where he used a pulsation code that includes treatment of non local convection and Eddington's approximation to radiative transfer (old code). Phorah (2007) improved on this code by replacing Eddington's approximation with radiative transfer by using the same non local convection theory (new code). Both codes show peaks in the luminosity amplitudes that correspond to depression in the damping rates. These were explained by Houdek (1996) as artifacts created by time dependent mixing length formalism and incomplete treatment of the non adiabatic effects. We also get similar value of the mean amplitude ratio of 0.2 ppm s cm-1 with both codes in the frequency range of 2.5 - 4.0 mHz. Comparisons of the theoretical mean amplitude ratios obtained with the two codes to the observed data show agreement in the frequency range of 2.5 - 4.0 mHz. We conclude that there are no significant differences between the codes when theoretical results are compared with the observational data in a given frequency range. In the second part of the thesis we use the median gravity mode period separation to search for Red Giant Clump (RGC) stars from a list of Red Giant (RG) stars in the Kepler field. The Kepler data used spans a period of 4 years starting in 2009. We construct echelle diagrams (plot of frequency versus frequency modulo large frequency separation) for some of the RG stars in NGC 6819, however, we are only able to identify 10 RGC single member (SM) stars in the Kepler open cluster NGC 6819. We measure the large frequency separation, 6.v and the frequency of maximum amplitude, Vmax for all the 10 RGC stars. We derive luminosities, radii, masses and distance moduli for each individual RGC star, from which we get the mean distance modulus of μ0 = 11.520±0.105 mag for the cluster when we use all the 10 RGC stars with reddening from the KIC. A value of μ0 = 11.747±0.086 mag is obtained when uniform reddening value E(B-V) = 0.15 is used for the cluster. The values of μ0 obtained are roughly in agreement with the values in the literature. A comparison of the observations with an isochrone of Age= 2.5 Gyr, Z = 0.017 with no mass loss using a statistical technique is made. A fractional mass loss of 7 ± 3 percent is obtained if we assume that no correction to 6.v between RC and red-giant branch (RGB) is necessary. However, models suggest that an effective correction of about 1.9 percent in 6.v is required to obtain the correct mass of RC stars owing to the different internal structure of stars in the two evolutionary stages. In this case we find that the mass loss in the red giant branch is not significantly different from zero. This finding is in agreement with the result of Miglio et al. (2012). It is clear that the mass estimate obtained by asteroseismology is not sufficient to deduce the mass loss on the red giant branch. The same approach of using median gravity mode period separation was also applied to another open cluster NGC 6866. We have found that based on the value of median gravity period separation, 6.P, KIC 8263801 is a Secondary Red Clump (SRC) star. In literature, no classification for this star has been provided. Doctoral