This textbook is geared toward beginning graduate students from a variety of disciplines whose primary focus is not necessarily mathematics for its own sake. Instead, A Probability Path is designed for those requiring a deep understanding of advanced probability for their research in statistics, applied probability, biology, operations research, mathematical finance, and engineering.
As far as math textbooks go, this one is pretty strong in the level of detail of the proofs (less handwaving than readers of Rudin will be used to). It even has a sense of humor at times! My main criticism is the insufficient examples given for some of the trickier measure theoretic concepts that can be difficult to intuit. For instance there isn't a single example of finding a conditional expectation with respect to a random variable, in the cases where the undergrad method of using the conditional density isn't going to cut it.