The International Gamma-Ray Astrophysics Laboratory, i.e. the INTEGRAL satellite of ESA, in orbit since about 3 years, performs gamma-ray observations of the sky in the 15 keV to 8 MeV energy range. Thanks to its imager IBIS, and in particular the ISGRI detection plane based on 16384 CdTe pixels, it achieves an excellent angular resolution (12 arcmin) for point source studies with good continuum spectrum sensitivity. Thanks to its spectrometer SPI, based on 19 germanium detectors maintained at 85 K by a cryogenic system, located inside an active BGO veto shield, it achieves excellent spectral resolution of about 2 keV for 1 MeV photons, which permits astrophysical gamma-ray line studies with good narrow-line sensitivity. In this paper we review some goals of gamma-ray astronomy from space and present the INTEGRAL satellite, in particular its instruments ISGRI and SPI. Ground and in-flight calibration results from SPI are presented, before presenting some selected astrophysical results from INTEGRAL. In particular results on point source searches are presented, followed by results on nuclear astrophysics, exemplified by the study of the 1809 keV gamma-ray line from radioactive 26 Al nuclei produced by the ongoing stellar nucleosynthesis in the Galaxy. Finally a review on the study of the positron-electron annihilation in the Galactic center region, producing 511 keV gamma-rays, is presented.