These notes are from a lecture course "Differentialgeometrie und Lie Gruppen" which has been held at the University of Vienna during the academic year 1990/91, again in 1994/95, and in WS 1997. It is not yet complete and will be enlarged during the year.
In this lecture course I give complete definitions of manifolds in the beginning, but (beside spheres) examples are treated extensively only later when the theory is developed enough. I advise every novice to the field to read the excellent lecture notes