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We present and describe im3shape, a new publicly available galaxy shapemeasurement code for weak gravitational lensing shear. im3shape performs amaximum likelihood fit of a bulge-plus-disc galaxy model to noisy images,incorporating an applied point spread function. We detail challenges faced andchoices made in its design and implementation, and then discuss variouslimitations that affect this and other maximum likelihood methods. We assessthe bias arising from fitting an incorrect galaxy model using simple noise-freeimages and find that it should not be a concern for current cosmic shearsurveys.  We test im3shape on the GREAT08 Challenge image simulations, and meet therequirements for upcoming cosmic shear surveys in the case that the simulationsare encompassed by the fitted model, using a simple correction for image noisebias. For the fiducial branch of GREAT08 we obtain a negligible additive shearbias and sub-two percent level multiplicative bias, which is suitable foranalysis of current surveys. We fall short of the sub-percent level requirementfor upcoming surveys, which we attribute to a combination of noise bias and themis-match between our galaxy model and the model used in the GREAT08simulations. We meet the requirements for current surveys across all branchesof GREAT08, except those with small or high noise galaxies, which we would cutfrom our analysis. Using the GREAT08 metric we we obtain a score of Q=717 forthe usable branches, relative to the goal of Q=1000 for future experiments. Thecode is freely available from https://bitbucket.org/joezuntz/im3shape

IM3SHAPE: A maximum-likelihood galaxy shear measurement code for cosmic gravitational lensing