These Lecture Notes are an expanded version of the Fermi Lectures I gave at Scuola Normale Superiore in Pisa, the Loeb Lectures at Harvard and the Whittemore Lectures at Yale, in 1978.  Meer

This paper is a contribution to the topological study of vector fields on manifolds. In particular we shall be concerned with the problems of exist­ ence of r linearly independent vector fields.  Meer