I Introduction and Examples.- II The Sequential Probability Ratio Test.- III Brownian Approximations and Truncated Tests.- IV Tests with Curved Stopping Boundaries.- V Examples of Repeated Significance Tests.- VI Allocation of Treatments.- VII Interval Estimation of Prescribed Accuracy.- VIII Random Walk and Renewal Theory.- IX Nonlinear Renewal Theory.- X Corrected Brownian Approximations.- XI Miscellaneous Boundary Crossing Problems.- Appendix 1 Brownian Motion.- Appendix 2 Queueing and Insurance Risk Theory.- Appendix 3 Martingales and Stochastic Integrals.- Appendix 4 Renewal Theory.- Bibliographical Notes.- References.

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