Thermodynamics, as is known, is constructed quite simply. Two of its main laws have been established experimentally, and by applying mathematical tools to them we can obtain the range of conclusions in which thermodynamics is so rich.The mathematical tools of thermodynamics are simple but in certain aspects at the same time quite sophisticated. Neglecting some of these sophisticated “trifles” often results in crude mistakes, even in reputable works on thermodynamics.The restricted size of the usual textbooks on thermodynamics does not permit discussing more extensively these important questions concerning the mathematical tools. For this reason it was felt neces­ sary to consider these problems in a special book, which though lim­ ited in size would at the same time go into details.Naturally, the author does not aim at a presentation of thermo­ dynamics and its physical, chemical, and technical applications. These have been sufficiently discussed in the existing textbooks and monographs. The purpose of this book is more modest—to deepen the reader’s knowledge of the mathematical tools of thermodynamics, to systematize them, and at the same time to emphasize questions that are often a source of error in thermodynamic calculations. The book is therefore designed to meet the needs of students and graduates majoring in thermal physics, physical engineering, and physico- technical specialities who already have a background in general thermodynamics. I hope that the book may also prove useful to scientists, engineers, and teachers specializing in thermodynamics.Comments on the contents of this book will be much appreciated.