High-resolution R, I, and H images of the center of Maffei 1, the nearest normal giant elliptical galaxy (M-V(0) = -20.9), have been acquired with the Hubble Space Telescope. At its distance of 3.0 Mpc, 1 pixel in the Planetary Camera field covers only 0.66 pc. The observations reveal that Maffei 1 is a "core type" elliptical galaxy, which is typical of intermediate to massive elliptical galaxies. A source of H emission has been discovered in the center. It is barely resolved, with a size of 1.2 pc and an ionized gas mass of only 29 M-circle dot. Dust is very prominent west of the center in a complex irregular pattern. The correlation between the reddening and the defficiency in surface brightness reveals that the dust is most likely Galactic in origin and that the reddening law along the line of sight is typical of that for the diffuse interstellar medium. For the first time, globular clusters have been detected. Twenty field sources show slightly or significantly extended profiles relative to foreground stars. In I the absolute magnitude of the brightest is -9.6, which is comparable to that of M3 in the Milky Way. The spread in R-I colors, as well the mean color, of these objects is greater than that found for Galactic globular clusters, which may be due in part to a metallicity difference compared with Galactic globular clusters and in part to the variable Galactic extinction across the Wide Field Planetary Camera 2 field. Fits of integrated analytic King models to three of the brighter candidates give core radii and concentration parameters that are comparable to those of Galactic globular clusters.