We present the first results from the science demonstration phase for the Hi-GAL survey, the Herschel key program that will map the inner Galactic plane of the Milky Way in 5 bands. We outline our data reduction strategy and present some science highlights on the two observed 2° × 2° tiles approximately centered at l = 30° and l = 59°. The two regions are extremely rich in intense and highly structured extended emission which shows a widespread organization in filaments. Source SEDs can be built for hundreds of objects in the two fields, and physical parameters can be extracted, for a good fraction of them where the distance could be estimated. The compact sources (which we will call cores' in the following) are found for the most part to b...