topology - Solving topological errors like invalid geometries in QGIS?

I use QGIS, version 2.18.9. I´ve several polygon-shapes with topological errors. Before I tried to apply the "intersection"-tool and got the message: Input layer A contains invalid geometries (feature 77). Unable to complete intersection algorithm. Firstly, I used the "check-validity"-tool, which detected some line-intersection and double nodes.

Then, I tried the "topology checker" with "must not have invalid geometries".

I´ve had the impression, that all errors where found then. So I applied the LWGEOM algorithms "Make valid" but got a error another messages ([error 87] falscher Parameter see log for more details).

I´m an absolute QGIS-beginner. So, I have not a single idea how to solve this problem. It has to be a simple automatically way, ´cause I´ve a big dataset here.