Analysis of information relationships is of primary importance for analysis and synthesis of digital information systems. This paper aims to introduce an discuss the fimdamental apparatus for the analysis and evaluation of information relationships. It defines and explains various relationships between information, measures for the amount and importance of information, and measures for the strength and importance of the information relationships. It demonstrates importance of the introduced relationships and measures for efficient synthesis, and shows how to apply them in the synthesis process. The analysis apparatus makes operational the famous theory of partitions and set systems of Hartmanis. While partitions and set systems enable us to model information, the relationships and measures enable us to analyze and measure information and information relationships. Both together form a complete information modeling and analysis apparatus that can be applied in logic design, decision system design, pattern recognition, knowledge discovery, machine learning and other areas.