Metrology is the science of measurements. It is traceable to measurement standards, thus to the concept of measurement accuracy, which is used in all natural and technical sciences, as well as in some fields of social sciences and liberal arts.The key problem is one of obtaining knowledge of the physical reality, which is observed through a prism of an assemblage of quantity properties describing the objectively-real world. One of the fundamental tasks of metrology is the development of theoretical and methodological aspects of the procedure of getting an accurate knowledge relating to objects and processes of the surrounding world.Due to the rapid development of information technologies and intelligent measurement systems and measuring instruments, as well as to the growing usage of mathematical methods in social and biological sciences, this monograph is dedicated to convey the fundamental theory.