The book is an introduction to actuarial mathematics and features new topics including an introduction to time diagrams and credibility theory, multi-state models and continuous time models. More complex types of contingent insurances will be featured and will include cases which involve durations or benefit amounts contingent on the time of the first death and will include applications on credit risk in life annuities. This new edition also includes additional material which is on the current syllabus of the Society of Actuaries examination on Life Contingencies. Furthermore a new chapter dealing with stochastic investment returns is also featured introducing the reader to various new ideas including the elements of option pricing.