This monograph and translation from the Russian describes in detail and comments on the fundamentals of metrology. The basic concepts of metrology, the principles of the International System of Units SI, the theory of measurement uncertainty, the new methodology of estimation of measurement accuracy on the basis of the uncertainty concept, as well as the methods for processing measurement results and estimating their uncertainty are discussed from the modern position. It is shown that the uncertainty concept is compatible with the classical theory of accuracy. The theory of random uncertainties is supplemented with their most general description on the basis of generalized normal distribution; the instrumental systematic errors are presented in connection with the methodology of normalization of the metrological characteristics of measuring instruments. The information about modern systems of traceability is given. All discussed theoretical principles and calculation methods are illustrated with examples.