Attempting to provide an ontological framework for the notion of the non-personal Universe of Being proposed elsewhere, this paper – after some basic definitions – focuses on substances, one pillar of that notion. It recognizes only to individual substances a material existence, viewed as the entire complex of the properties instantiated in each of them. It then examines features of the general essence of substances. While such essence can be comprehended via abstract definitions, their individual essence cannot, I argue, because (...) it is not a concept but a reality, which I refer to as Being. This manifests powers, is inexhaustible growth and is one, although expressed differently in each individual. The possible connection of the human being with this reality is the second pillar of the notion of the non-personal Universe of Being, which I summarize and compare to other scenarios at the end. (shrink)