One of the main aims of this book is to clarify - at the level of basic information - to the readership interested for any reason in Mathematics and mathematics education, exactly what Functional Equations are, what real scientific and practical problems they arose from, and who is their role in the development of mathematics and other sciences. Highlighting the role and importance of Functional Equations as a teaching tool is connected to our effort for its harmonious inclusion in the body of school Mathematics and by extension in the first years of studies at A.E.I. and A.T.E.I.