This monograph concerns nomological necessity and possibility, where such constraints of necessity are the laws of nature. It presumes that in reality, in this fundamentally physical world, these are fundamental physical laws. This text appeals to philosophers, physicists and students. Its central topic is physical possibility and necessity. The primary thesis of this book is that physical necessity and possibility are determined by a so-called 'modal structure', and indeed a modal structure that is rooted in actuality in a certain way, and so is a 'rooted modal structure'. Developing this primary thesis hence also involves developing an account of the fundamental nature of the actual physical world, which itself is constituted in entirety by a complicated form of rooted modal structure. That is the second key thesis of the text. It is developed by an exploration in historical sequence of four conceptions of fundamental physical mechanics.