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The stratosphere is the highest layer of Earth's atmosphere where aircraft can still fly. The density of the air is just high enough here to generate lift on a wing or buoyancy on a balloon, so designing any stratospheric aircraft is a delicate technological balancing act for the engineer. Designing and operating an aircraft capable of conveying humans to the stratosphere is more challenging still: biologically, we simply do not belong up there. Temperatures often as low as -80C (-112F) and an ambient pressure rapidly diminishing with altitude make for an extremely forbidding environment. In fact, as we pass 50 000 feet (the lower end of Concorde's cruising altitude range), we enter the space equivalent zone - from a physiological point of view we might as well be in low Earth orbit. The fact that stratospheric flight is possible at all - moreover, even safe and economical, at least in the lower stratosphere - is made possible by some relatively recent advances in our understanding of the science of high altitude flight. This book charts some of these developments; at the same time, it is a catalog of ways in which the stratosphere can catch out even the well-prepared flyer. Naturally, the failures of early explorers have signposted many of these dangers, but, as regular news headlines and the series of vignettes that punctuate the book illustrate, the learning curve has not levelled off, it has merely become shallower. Stratospheric flight is still aviation at the limit.