The main topic in this book is so-called observation theory. The aim is to reconstruct complete information about a solution of a non-linear system of ordinary differential equations (depending in general on a parameter u in Rd, possibly coupled to a system of functional equations in the same variables) from the knowledge of suitable partial data. The authors introduce a new concept of observability (resp. strong observability). The character of the problem depends strongly on a relation between the number of functional equations and the dimension of the parameter u, and develop a systematic method for treating such problems. The methods used include transversality theorems, the theory of subanalytic sets, Whitney stratification results, some facts from several complex variables and Lyapunov’s theorems. The book ends with two applications in chemical engineering, and will be of interest to researchers in control theory.