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.