This book combines Descartes famous Discourse on Method along with some polite correspondence letters written to its critics, as well as two other publications: Rules for Guiding One's Intelligence in Searching for the Truth and a portion of The World.
The Discourse on Method itself is a must-read for students of philosophy, mathematics or any of the sciences (especially engineering or computer science), as it defines indispensable ground rules for problem-solving. He establishes some basic rules now common to engineering, such as, never accepting something to be true unless you know it to be true, dividing a problem into as many smaller manageable pieces as necessary to resolve it efficiently, attacking all the pieces of a problem at the simplest pieces first, and to meticulously document/enumerate the processes and solution as you go. The latter portions of this discourse focus on the philosophical question of man's most irreducible elements, searching for a definition of the soul. From this portion you get the famous phrase "I think therefore I am".
The excerpts from The World, were not terribly interesting, but this owes more to the fact that it is severely dated. There were some portions of it that lightly referenced the heliocentric theory which caused Descartes to hold off publication until after his death, once he saw how the church reacted to Galileo's publications. But again, many of the postulations are dated and based on a 17th century view of matter, physiology, and astronomy.
The Rules for Guiding One's Intelligence in Searching for the Truth can be thought of as an detailed extension of the techniques outlined in Discourse on Method and is perhaps much more suited to students or professionals whose line of work requires day-to-day implementation of the scientific method. His view is that "mathematical studies" should be more than just the narrow categorization in which we've come to see arithmetic and geometry. Instead it should imply any study or technique that deals with order or measure, regardless if it deals with numbers, figures, stars, sounds or something else. He felt that this broader definition is what was understood by the Greeks who studied under Pythagoras & Plato, who had prerequisite for any potential student to have an understanding of "mathesis". He enumerates twenty-one rules that constitute this understanding of mathematical practice, much of which is now the basis of the modern scientific method, specifically related to defining and developing a hypothesis. It is incredibly useful publication that I can see myself coming back to and re-reading often in the future.