We present the first results of a study of the stellar population in a region of 30 pc radius around SN 1987A, based on an analysis of multiband Hubble Space Telescope (HST) WFPC2 images. The effective temperature, radius and, possibly, reddening of each star were determined by fitting the measured broadband magnitudes to the ones calculated with model atmospheres. In particular, we have determined effective temperatures and bolometric luminosities for 21,995 stars, and for a subsample of 2510 stars we also determined individual reddening corrections. In addition, we have identified all stars with Hα equivalent widths in excess of 8 Å, a total of 492 stars. An inspection of the H-R diagram reveals the presence of several generations of young stars, with ages between 1 and 150 Myr, superposed on a much older field population (0.6-6 Gyr). A substantial fraction of young stars with ages around 12 Myr make up the stellar generation coeval to SN 1987A progenitor. The youngest stars in the field appear to be strong-line T Tauri stars, identified on the basis of their conspicuous (Weq > 8 Å) Hα excesses. This constitute the first positive detection of low-mass (about 1-2 M☉) pre-main-sequence (PMS) stars outside the Milky Way. Their positions in the H-R diagram appear to require that star formation in the LMC occurs with accretion rates about 10 times higher than in the Milky Way, i.e., ~10-4M☉ yr-1. SN 1987A appears to belong to a loose, young cluster 12 ± 2 Myr old, in which the slope of the present mass function is almost identical to Salpeter's, i.e., Γ = d log N/d log M ≃ -1.25 for masses above 3 M☉, but becomes much flatter for lower masses, i.e., Γ ≃ -0.5. On a large scale, we find that the spatial distributions of massive stars and low-mass PMS stars are conclusively different, indicating that different star formation processes operate for high- and low-mass stars. This results casts doubts on the validity of an initial mass function (IMF) concept on a small scale (say, less than 10 pc). Moreover, it appears that a determination of the low-mass end IMF in the LMC requires an explicit identification of PMS stars. A preliminary analysis, done for the whole field as a single entity, shows that the IMF slope for the young population present over the entire region is steeper than Γ ≃ -1.7.