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Synopsis According to a remark attributed to Mark Kac, probability theory is measure theory with a soul. Furthermore, measure theory has its own ramifications in topics like function spaces, Operator theory, generalized functions, ergodic theory, group representations, quantum probability etc. On the other hand recent explosive developments in the applications of probability theory have imposed the need for a good grasp of measure theory among a wide spectrum of scholars ranging from economists to engineers and physicist to psychologists. This book with its choice of proofs, remarks, examples and exercises has been prepared taking both these aesthetic and practical aspects into account. Courses based on this book will help undergraduate and graduate students in getting a firm grasp of the fundamentals in the twin themes of probability and measure.