We present a catalog of 536 fast radio bursts (FRBs) detected by the Canadian Hydrogen Intensity Mapping Experiment Fast Radio Burst (CHIME/FRB) Project between 400 and 800 MHz from 2018 July 25 to 2019 July 1, including 62 bursts from 18 previously reported repeating sources. The catalog represents the first large sample, including bursts from repeaters and non-repeaters, observed in a single survey with uniform selection effects. This facilitates comparative and absolute studies of the FRB population. We show that repeaters and apparent non-repeaters have sky locations and dispersion measures (DMs) that are consistent with being drawn from the same distribution. However, bursts from repeating sources differ from apparent non-repeaters in intrinsic temporal width and spectral bandwidth. Through injection of simulated events into our detection pipeline, we perform an absolute calibration of selection effects to account for systematic biases. We find evidence for a population of FRBs - comprising a large fraction of the overall population - with a scattering time at 600 MHz in excess of 10 ms, of which only a small fraction are observed by CHIME/FRB. We infer a power-law index for the cumulative fluence distribution of $alpha=-1.40pm0.11(textrm{stat.})^{+0.06}_{-0.09}(textrm{sys.})$, consistent with the $-3/2$ expectation for a non-evolving population in Euclidean space. We find $alpha$ is steeper for high-DM events and shallower for low-DM events, which is what would be expected when DM is correlated with distance. We infer a sky rate of $[820pm60(textrm{stat.})^{+220}_{-200}({textrm{sys.}})]/textrm{sky}/textrm{day}$ above a fluence of 5 Jy ms at 600 MHz, with scattering time at $600$ MHz under 10 ms, and DM above 100 pc cm$^{-3}$.
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