TOC: I Description of Formal Mathematics: Terms and relations; Theorems; Logical theories; Quantified theories; Equalitarian theories.- II Theory of Sets: Collectivizing relations; Ordered pairs; Correspondences; Union and intersection of a family of sets; Product of a family of sets; Equivalence relations.- III Ordered Sets, Cardinals, Integers: Well-ordered sets; Equipotent sets; Cardinals. Natural integers. Finite sets; Properties of integers; Infinite sets; Inverse limits and direct limits.- IV Structures: Structures and isomorphisms; Morphisms and derived structures; Universal mappings