We present the first event-horizon-scale images and spatiotemporal analysis of Sgr A^* taken with the Event Horizon Telescope in 2017 April at a wavelength of 1.3 mm. Imaging of Sgr A^* has been conducted through surveys over a wide range of imaging assumptions using the classical CLEAN algorithm, regularized maximum likelihood methods, and a Bayesian posterior sampling method. Different prescriptions have been used to account for scattering effects by the interstellar medium toward the Galactic center. Mitigation of the rapid intraday variability that characterizes Sgr A^* has been carried out through the addition of a “variability noise budget” in the observed visibilities, facilitating the reconstruction of static full-track images. Our static reconstructions of Sgr A^* can be clustered into four representative morphologies that correspond to ring images with three different azimuthal brightness distributions and a small cluster that contains diverse nonring morphologies. Based on our extensive analysis of the effects of sparse (u, v)-coverage, source variability, and interstellar scattering, as well as studies of simulated visibility data, we conclude that the Event Horizon Telescope Sgr A^* data show compelling evidence for an image that is dominated by a bright ring of emission with a ring diameter of ∼50 μas, consistent with the expected “shadow” of a 4 × 10⁶ M_☉ black hole in the Galactic center located at a distance of 8 kpc.