Actuarial science is peculiarly dependent upon the Theory of Probabilities, the solution of many of its problems is best effected by resort to the Differential and Integral Calculus and in practical work the Calculus of Finite Differences is almost indispensable. Excellent text-books on these subjects are, of course, available but none of them has been written with the special requirements of the actuary in view. In beginning his training the student is, therefore, confronted by the difficulty of judicious selection and in the circumstances it has appeared to the Council of the Institute of Actuaries that a mathematical text-book sufficiently comprehensive, with the standard works on Higher Algebra, to provide the ground-work of an actuarial education would be of great value. At the request of the Council, Mr Alfred Henry has undertaken the preparation of such a work and the resulting volume is issued in the confident expectation that it will materially lighten the toil of those who essay to qualify themselves for an actuarial career.