The Near Infrared Imager and Slitless Spectrograph (NIRISS) aboard the James Webb Space Telescope (JWST) will offer wide-field slitless spectroscopy (WFSS) with a resolving power R = 150 at wavelengths from 0.8 to 2.25 microns. In this band, NIRISS will be sensitive to Lyman α emission lines and continuum breaks in the spectra of galaxies with redshifts 6 < z < 17, allowing it to probe the first stars and ionizing sources in the early universe. NIRISS observations of the high-redshift universe will provide a wealth of information on foreground objects, creating a unique library of optical emission-line spectra from the faintest galaxies at lower redshifts. To explore its ability to identify and characterize galaxies at all redshifts, we have modeled a NIRISS observation of a massive strong-lensing galaxy cluster and analyzed the synthetic images using standard software tools. Our simulations demonstrate that WFSS with NIRISS will provide a powerful tool for the exploration of galaxies near and far.