Course outline The content of the present course splits into two parts lectured by Myles Workman and Ulrich Menne, respectively.

1. Grassmann algebra (the exterior algebra of a vector spaces, alternating algebra of a vector space, (alternating forms and duality, interior multiplications, simple m-vectors, inner products) and
2. rectifiability comprised of
   • Rademacher's theorem,
   • factorisation near generic points,
   • submanifolds of Euclidean space (submanifolds, tangent vectors, relative differentiation), and
   • area for Lipschitzian maps (Jacobians, area of maps of Euclidean space, rectifiable sets, approximate tangent vectors and differentials, area of maps of rectifiable sets, Cartesian products, equality of measures on rectifiable sets, and rectifiable sets and manifolds of class 1).

Jointly, these parts provide the necessary infrastructure to develop (in possible subsequent courses) the theory of sets of finite perimeter, integral currents, or integral varifolds.

Details of the course The main reference text will be the instructors’ weekly updated lecture notes written in LATEX, see [Men25]. They are based on and expand the relevant parts of Federer’s treatise [Fed69]. Grading is solely determined by individual oral examinations conducted in English.

Prerequisites We continue the courses Geometric Measure Theory (I) which treated covering theorems, derivatives, Carathéodory's construction, and differentiation and the course Special Topics in Analysis which treated Borel sets, multilinear algebra, higher order differentiation, and pointwise differentiability theory.