The subject of concave analysis involves both concave and convex functions and their generalizations. The aim of the book is to provide a basic and self-contained introduction to concepts and detailed study of concave and convex functions. It is written in the style of a textbook, designed for courses in mathematical economics, finance, and manufacturing design. The suggested prerequisites are multivariate calculus, ordinary and elementary PDEs, and elementary probability theory. Depending on the curriculum at different universities and colleges, this book will probably be useful to senior undergraduate students but definitely beginning graduate students in the above disciplines.