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We present first results from the third GRavitational lEnsing AccuracyTesting (GREAT3) challenge, the third in a sequence of challenges for testingmethods of inferring weak gravitational lensing shear distortions fromsimulated galaxy images. GREAT3 was divided into experiments to test threespecific questions, and included simulated space- and ground-based data withconstant or cosmologically-varying shear fields. The simplest (control)experiment included parametric galaxies with a realistic distribution ofsignal-to-noise, size, and ellipticity, and a complex point spread function(PSF). The other experiments tested the additional impact of realistic galaxymorphology, multiple exposure imaging, and the uncertainty about aspatially-varying PSF; the last two questions will be explored in Paper II. The24 participating teams competed to estimate lensing shears to within systematicerror tolerances for upcoming Stage-IV dark energy surveys, making 1525submissions overall. GREAT3 saw considerable variety and innovation in thetypes of methods applied. Several teams now meet or exceed the targets in manyof the tests conducted (to within the statistical errors). We conclude that thepresence of realistic galaxy morphology in simulations changes shearcalibration biases by $\sim 1$ per cent for a wide range of methods. Othereffects such as truncation biases due to finite galaxy postage stamps, and theimpact of galaxy type as measured by the S\'{e}rsic index, are quantified forthe first time. Our results generalize previous studies regarding sensitivitiesto galaxy size and signal-to-noise, and to PSF properties such as seeing anddefocus. Almost all methods' results support the simple model in which additiveshear biases depend linearly on PSF ellipticity.

GREAT3 results I: systematic errors in shear estimation and the impact of real galaxy morphology