Foreword to the Revised Edition -- First order predicate logic with choice operator -- First order term logic with choice operator -- Embedding of predicate logic in term logic -- Embedding of term logic in predicate logic -- Free occurence of a variable. Rank of term. Elementary substitution -- A term calculus -- Soundness of the rules -- Survey of the completeness proof -- Some theorems concerning deducibility -- Substitution -- Further theorems concerning deducibility -- Survey of the proof of the Theorem on satisfiability -- Details of the proof -- Completeness of restricted term calculus.