ISLA--the International Stratospheric Laboratory for Astrophysics--is proposed as the consequential evolution from present ground- and space-based astronomical observatories. ISLA operates remotely controlled at approximately 15 km altitude. Its diffraction limited 4 m telescopes permit imaging with 30 milli-arcsec resolution, while the interferometric combination of its telescopes reaches milli-arcsec resolution. The extremely low residual water vapor allows nearly unhindered observations from the infrared to the sub-mm spectral range. The efficiency of imaging and spectroscopy increases by about 103, due to the improved light concentration, and interferometric observations will even be facilitated by factors of 104 to 105 compared to ground-based observations. ISLA combines the advantages of modern pressurized balloons with those of rigid airships. Several diffraction limited, extremely light telescopes of 2 to 4 m diameter are stationed on ISLA, together with the optics necessary for interferometry. The size and numbers of telescopes on ISLA will surpass any present and realistic future space telescope projects. The advantages of easy maintenance and exchange of instrumentation assure that the ISLA observatory will permanently be at the state of art. Scientific challenges to be tackled with ISLA are the search for extra-solar planets, details of star forming regions, surfaces of giant stars, nuclei of galaxies, gravitational lenses and the evolution of novae and supernovae etc. Many more presently unasked important scientific questions will arise than can be answered, but most likely there will be fascinating totally unexpected discoveries from ISLA.