This small volume is the English edition of a Japanese book entitled "Learning fluid dynamics from dolphins". The title is derived from the fact that "Dolphins swim too fast to be explained scientifically". The first person to clearly describe this phenomenon was the English biologist Sir James Gray (J.Gray, 1936), and this mystery is known among physicists and specialists in marine engineering as "Gray's paradox" or simply as the "Mystery of dolphins". In addition to dolphins, tuna, marlin and some other fish are also famous for swimming at extraordinary high speeds. Treating both dolphins and fish together in the same title is difficult because both animals have far different taxonomy - dolphins belonging to oceanic mammals and tuna and marlin belonging to teleostei fish. This book uses dolphins as symbolic animals that perform high-speed swimming. Furthermore, "dolphins" are chosen as the main co-actor in this English edition because western readers feel an affinity for them. This book focuses on readers, who are interested in technology and science and who hope to specialize in technological occupations. This book aims to introduce the developing history of fluid dynamics, and then outlines the research history and the present recognition of "Gray's paradox". Finally, the author's research, through about three decades, is reviewed. This paradox suggested in the early 20th century has carried over into the 21st century without finding a complete solution. It would be a great pleasure for the author if the readers find interest in fluid dynamics, a discipline that has developed by overcoming numerous paradoxes, or feel the mood at the forefront of the "intelligence" of mankind.