A new realist interpretation of quantum mechanics is introduced. It is shown that quantum systems have two different kinds of properties: the usual ones described by values of quantum observables, which are called extrinsic and the real ones, which are called intrinsic. The existence of intrinsic properties, usually denied by textbooks, is suggested by everyday praxis of quantum mechanics. They do form a sufficiently large set and can be classified into structural and modal. The new approach contributes to the foundations of statistical physics and to the problems of classical properties and quantum measurement. Classical properties are some intrinsic properties of the underlying quantum systems. A general self-consistent framework for quantum theory of classical properties is proposed and illustrated by an example. All existing theoretical models of measuring apparatuses are shown to be incompatible with our approach. New principles according to which better models could be constructed are illustrated by another example.