A physical measurement is meaningful only if one identifies in a non-ambiguous way who is the observer and what is being observed. The same observable can be the target of more than one observer so we need a suitable algorithm to compare their measurements. This is the task of the theory of measurement which we develop here in the framework of general relativity.
Before tackling the formal aspects of the theory, we shall define what we mean by observer and measurement and illustrate in more detail the concept which most affected, at the beginning of the twentieth century, our common way of thinking, namely the relativity of time.
We then continue on our task with a review of the entire mathematical machinery of the theory of relativity. Indeed, the richness and complexity of that machinery are essential to define a measurement consistently with the geometrical and physical environment of the system under consideration.
Most of the material contained in this book is spread throughout the literature and the topic is so vast that we had to consider only a minor part of it, concentrating on the general method rather than single applications. These have been extensively analyzed in Clifford Will's book (Will, 1981), which remains an essential milestone in the field of experimental gravity. Nevertheless we apologize for all the references that would have been pertinent but were overlooked.