Probability theory is an important part of contemporary mathematics. The subject plays a key role in the insurance industry, modelling financial markets, and statistics generally -- including all those fields of endeavour to which statistics is applied (e.g. health, physical sciences, engineering, economics, social sciences). The twentieth century haeen an important time for the subject because we have witnessed the development of a solid mathematical basis for the study of probability, especially from the Russsian school of probability under the leadership of A.N. Kolmogorov. We have also seen many new applications of probability including applications of stochastic calculus in the finance industry, fundamental ideas in computer science, and internet gambling.