Barwise and Seligman's recent theory of information flow and the logic of distributed systems (IIF) has received widespread attention. The theory aims to provide a mathematical framework which models the flow of information in distributed systems with connected components i.e how remote objects, situations and events carry information about one another. The basic standpoint of this theory is that each part or constituent component of a distributed system is represented by a classification, i.e. a collection of objects together with a collection of yes/no properties of these objects, and that the classifications are connected with information-preserving connections called infomorphisms. The primary contribution of this thesis lies in its departure from the basic assumption that properties of objects are yes/no properties. We allow more general properties, namely, graded properties, which apply to objects to degrees such as, 0, 0.4, 0.8, 1 etc., rather than 0 and 1 only. The main aim is to make Barwise and Seligman's theory more realistic since, more often than not, properties of real-world systems are graded rather than yes/no. We study the basic concepts of the theory of information flow and present results in the graded framework. Namely, we study the concepts of a classification, infomorphism and channel. We present several theorems for these concepts in the graded framework which allow us to generalize the theorems of the classical theory of information flow. Moreover, the theorems elucidate that in the graded framework, the phenomenon of information flow is graded, too. We include examples which demonstrate the concepts and the results.