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Concordance cosmology points to a Universe of zero mean curvature, due to theinflation mechanism which occurred soon after the Big Bang, while along arelatively small number of lower redshift light paths where lensing events areobserved, space is positively curved. How do we know that global geometry andtopology are robust rather than in a state of chaos? The phenomenon of cosmicshear provides an effective way of mapping curvature fluctuations, because itaffects {\it any} light rays whether they intercept mass clumps or not. Wediscuss a range of astrophysical applications of the principal manifestation ofshear - the distortion of images. It will be shown that the quickest way oftesting the existence of shear in the near Universe is to look at the shape ofEinstein rings. The fact that most of these rings are circular to a largeextent means, statistically speaking, shear occurs at a much lower level thanthe expectation based upon our current understanding of the inhomogeneousUniverse. While inflation may account for the mean geometry, it offers no meansof stabilizing it against the fluctuations caused by non-linear matter clumpingat low redshift. Either this clumping is actually much less severe, or thephysical mechanism responsible for shaping the large scale curvature has beenactive not only during the very early epochs, but also at all subsequent times.Might it be the vital `interface' between expansion on Hubble distances andgravity on cluster scales and beneath?

On the absence of shear from perfect Einstein rings and the stability of geometry