A complete theory of measurement from the principles of establishing the reality images to measurement procedures is presented in this book. A precise mathematical model of errors is presented with the use of various applications to interpret measurement results. Axioms are formulated which provide a deduction theory of measurement. The variety of problems addressed by modern science results in a diversity of models of physical and metrological phenomena, and leads to the view that there is not now, and may never be, a uniform theory of measurement. There is a need, however, to establish a foundation common to all measurements and studies, and this is the author's main aim allied to attempts to create a universal theory of measurement. The purpose of measurement is discussed. Many practical examples illustrating the methodology of modelling, calibration and the analysis of the results of measurement are reviewed. The book is designed for physicists, analytical and physical chemists and engineers involved with the work of metrology. A knowledge of physics, probability and statistics and the principles of metrology is a prerequisite for understanding this work.