In preparing the manuscript, I have had the benefit of the valued criticism of my colleagues, Professors E. E. Van Vleck and L. W. Dowling, and of Mr. L. A. Anderson, Actuary for the Wisconsin Insurance Department. Professor Arnold Dresden, Dr. Florence Allen, Dr. G. R. Clements, and Mr. T. M. Simpson, who have tried out a large part of the material in the class room, have made many helpful suggestions in the selection of material and examples, and have rendered valuable assistance in verifying worked-out examples and in correcting proofs. I am also under obligations to Professor D. F. Campbell, of Armour Institute, for placing at my disposal notes and other material relating to the elements of the theory of life insurance.