Hartig net is a hyphal network, that extends into the root, penetrating between the epidermal and cortical cells of ectomycorrhizal plants. This network is a site of nutrient exchange between the fungus and the host plant.
The early research on the anatomy of the interface between ectomycorrhizal fungi and plants was done by Robert Hartig, a 19th-century German plant pathologist, so the Hartig net is named after him.
References
Hartig net Wikipedia(Text) CC BY-SA