We will talk about analysis on fractal spaces. While "second order differential operators" and related elliptic and parabolic equations have now been understood for quite some time, an understanding of "first order differential operators" and first order equations on fractals is still at the very beginning.

We will give a short introduction and then explain recent results, joint with Waldemar Schefer (Bielefeld University). These results generalize earlier results of Hino, Strichartz and others and led to novel integration by parts formulas and to first well-posedness results for equations of continuity type on fractals.