We present the first year of Hubble Space Telescope imaging of the unique supernova (SN) Refsdal, a gravitationally lensed SN at z=1.488$pm$0.001 with multiple images behind the galaxy cluster MACS J1149.6+2223. The first four observed images of SN Refsdal (images S1-S4) exhibited a slow rise (over ~150 days) to reach a broad peak brightness around 20 April, 2015. Using a set of light curve templates constructed from SN 1987A-like peculiar Type II SNe, we measure time delays for the four images relative to S1 of 4$pm$4 (for S2), 2$pm$5 (S3), and 24$pm$7 days (S4). The measured magnification ratios relative to S1 are 1.15$pm$0.05 (S2), 1.01$pm$0.04 (S3), and 0.34$pm$0.02 (S4). None of the template light curves fully captures the photometric behavior of SN Refsdal, so we also derive complementary measurements for these parameters using polynomials to represent the intrinsic light curve shape. These more flexible fits deliver fully consistent time delays of 7$pm$2 (S2), 0.6$pm$3 (S3), and 27$pm$8 days (S4). The lensing magnification ratios are similarly consistent, measured as 1.17$pm$0.02 (S2), 1.00$pm$0.01 (S3), and 0.38$pm$0.02 (S4). We compare these measurements against published predictions from lens models, and find that the majority of model predictions are in very good agreement with our measurements. Finally, we discuss avenues for future improvement of time delay measurements -- both for SN Refsdal and for other strongly lensed SNe yet to come.
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