So I am following a Tutorial in making an anvil. I baked a normal map, but all a get from it are some ugly black spots, that disappear when I disconnect the normal map node. I guess theres someting wrong with the nodes, but I don´t know what. Bumps like on the anvil in the background only appear in the render. Any ideas?
You should almost certainly not be using a strength of 10 in your normal map node. The default strength of 1.0 is usually appropriate. 10 is very, very high.
You should be reading your normal map as non-color data rather than sRGB data. It should also have been baked as non-color data. (In theory, it should be okay to read the normals as sRGB if they were baked as sRGB, but in my experience, it doesn't actually work that way, not in Blender.)
The places where your normal map image is not sorta lavender-- the places where the blue channel is <0.5-- are places where your low poly didn't enclose the high poly, and so its rays hit the other side of the anvil. Those normals are not the normals you want. Increase ray extrusion to place the origin of the rays further from the low poly, so that the rays in these locations hit the correct side of the anvil.