This specialized monograph is devoted to a detailed study of functional equations of the form g(x, f(x), f(F1(x)), …, f(Fn(x)))=0 on the real line R or on the unit circle T. Here f is an unknown function, Fk, k = 1,…,n, are given mappings from R or T into itself and g is a given mapping into R. The equation includes various equations studied in literature as special cases. Two main questions studied are local solvability at every point and the global solvability of the equation. The content can be characterized by names of chapters: Implicit functions (a special case), Classification of one-dimensional mappings, Generalized Abel equations, Equations with several transformations of argument and Linear equations. This carefully written condensed text is accompanied by numerous examples. It contains new results and concepts, which may be applied also to multidimensional functional equations. The book will be of interest for specialists in functional equations as well as for those working in related fields. It can be recommended for libraries.