Algorithm for computing the moduli space of pointed Gorenstein curves with Weierstrass gap sequence \(1,2,\ldots,g-2,\lambda,2g-3\) Torsors, étale homotopy and applications to rational points. Lecture notes of mini-courses presented at the workshop ``Torsors: theory and applications'', Edinburgh, UK, January 10--14, 2011 and at the study group organised in Imperial College, London, UK in autumn 2010 