This book, written by the outstanding Russian philosopher and logician A. A. Zinoviev, provides a systematic presentation of the formal apparatus of complex logic developed by the author. The general theory of deduction and its extensions are considered, including the theory of predication, quantifiers, conditionals, modalities, existence, norms, terms, relations and physical implication. The author provides evidence of the consistency and completeness of systems of complex logic with respect to certain semantic interpretations, clarifies the place of classical and intuitionistic logics in the theory of logical implication. Recommended for philosophers, logicians, scientific methodologists, students and graduate students of relevant specialties.