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Probability theory is a well-established branch of Mathematics that finds applications in a wide area of scholarly activities such as in Physics, Chemistry, Geology, medicine, economics, sociology, engineering, operation research, etc. With his insightful exploration of the probabilistic connection between philosophy and the history of science, John Maynard Keynes, perhaps the best known of economists, breathed new life in the study of both these disciplines. His a treatise on probability is an outstanding mathematical work and is widely considered as an important contribution to the theory regarding the logical probability of proportions. What Keynes wrote is sacrosanct and has been retained in this book. His original book is in 31 chapters. In order to facilitate updating, we have combined some chapters and presented it in 26 chapters and converted it into third person from the original first person, keeping in view the modern trend. We have added important developments that have taken place since Keynes wrote the book, to provide updated material to the students and teachers of various disciplines. The book is divided into five parts. Part-i provides fundamental ideas on probability. Part-ii contains fundamental theorems. Br>part-iii deals with Induction and analogy. Br>part-iv throws light on some philosophical applications of probability, while br>Part-V relates to the foundations of statistical inference. Bibliography has been updated by including more books. Index also stands revised and updated. Exclusive chapters ‘practice problems’ have been added in each part except br>Part-IV, containing a large number of solved exercises providing plenty of opportunity to the students for practicing skills and developing a sound understanding of the subject. Unsolved exercises have been given under ‘test yourself’. the book with updated matter and in its present layout will be useful for students and teachers of various disciplines including economics, physical sciences, engineering, Geology, statistics, economics and sociology.