This will be the first in a series of lectures. An outline is as follows: sheaf cohomology via Cech (GH=Griffiths-Harris 0.3) sheaves on P^n - cohomology and dictionary with modules (e.g. Hartshorne p225) spectral sequences and hypercohomology (GH 438-454) Belinson theorem (Okonek-Spindler-Schneider p239-246) application to spaces of matrices of constant rank