We present the initial results of a study of globular clusters in M 31, using the Faint Object Camera (FOC) on the Hubble Space Telescope (HST). The sample of objects consists of 13 clusters spanning a range of properties. Three independent image deconvolution techniques were used in order to compensate for the optical problems of the HST, leading to mutually fully consistent results. We present detailed tests and comparisons to determine the reliability and limits of these deconvolution methods, and conclude that high-quality surface photometry of M 31 globulars is possible with the HST data. Surface brightness profiles have been extracted, and core radii, half-light radii, and central surface brightness values have been measured for all of the clusters in die sample. Their comparison with the values derived from ground-based observations indicates the later to be systematically and strongly biased by the seeing effects, as it may be expected. A comparison of die structural parameters with those of the Galactic globulars shows that the structural properties of the M 31 globulars are very similar to those of their Galactic counterparts. A candidate for a post-core-collapse cluster, Bo 343 = G 105, has been already identified from these data; this is the first such detection in die M 31 globular cluster system.