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abstract: 'In the course of conducting a deep ($14.5 \la r \la 23$), 20 night survey for transiting planets in the rich $\sim 550$ Myr old open cluster M37 we have measured the rotation periods of 575 stars which lie near the cluster main sequence, with masses $0.2 M_{\odot} \lesssim M \lesssim 1.3 M_{\odot}$. This is the largest sample of rotation periods for a cluster older than $500~{\rm Myr}$. Using this rich sample we investigate a number of relations between rotation period, color and the amplitude of photometric variability. Stars with $M \ga 0.8 M_{\odot}$ show a tight correlation between period and mass with heavier stars rotating more rapidly. There is a group of 4 stars with $P > 15~{\rm days}$ that fall well above this relation, which, if real, would present a significant challenge to theories of stellar angular momentum evolution. Below $0.8 M_{\odot}$ the stars continue to follow the period-mass correlation but with a broad tail of rapid rotators that expands to shorter periods with decreasing mass. We combine these results with observations of other open clusters to test the standard theory of lower-main sequence stellar angular momentum evolution. We find that the model reproduces the observations 