Chapter ¿1. Preparations from probability theory.- Chapter 2. Martingale with discrete parameter.- Chapter 3. Martingale with continuous parameter.- Chapter 4. Stochastic integral.- Chapter 5. Applications of stochastic integral.- Chapter 6. Stochastic differential equation.- Chapter 7. Application to finance.- Chapter 8. Appendices.- References.

The author is currently Professor Emeritus at The University of Tokyo and visiting Professor at Meiji University. He previously held positions at The University of Tokyo and Research Institute for Mathematical Sciences, Kyoto University. He was an invited speaker at the ICM 1990.