Radio sky surveys using single-dish radio telescopes are conducted at frequencies ranging from 300 MHz to 857 GHz. Examples include the WMAP and Planck cosmic microwave background satellites, C-BASS, and the GMIMS polarization survey which uses Penticton in Canada. In all such surveys, the telescope measures the brightness distribution of the radio emission convolved with the radiation pattern of the telescope. For map-making, the sky is pixelated so that the measured data is distributed on the pixelated sky. However, the telescope scans the sky in a random pattern irrespective to the pixelated sky. So, in practice, the data measured is binned to the nearest pixel centre on the pixelated sky, where the pixel size is less than the telescope beam. This method, however, increases the noise in the resultant map and ignores the fact that the sky is a continuous function. In this thesis, we develop an interpolation-based map-making algorithm which takes into consideration the continuous sky function, so that a weighted intensity of the measured data is assigned to each pixel. The algorithm uses the ideal pixelization scheme HEALPix with a Gaussian distribution as the weight function. The all-sky map produced is less noisy than one made by binning but is computationally expensive. We report a standard deviation of 2.33 x10^-4 for the difference map and 2.78 x10^-3 for the smoothed binning map and a standard deviation of 2.23 x 10^-4 for the difference map and 2.7 x 10^-4 for the grid interpolation map. This dissertation is also extended to develop an elliptical interpolation function to approximately circularize an elliptical telescope beam.