The thermodynamic formulas most often used in theoretical and practical work state various relations between first and second derivatives of various thermodynamic functions. There are a very large number indeed of such relations, and the discovery of the one needed in any particular problem usually takes considerable time, especially if one is not working continually in the field. In this collection of formulas, means have been found for condensing into very small space all the possible relations of this character. A number of problems are worked in detail, illustrating various uses of the formulas, and methods are described of extending the formulas to systems exposed to more general external forces than the conventional hydrostatic pressure.