The approximation of functions by linear positive operators is an important research topic in general mathematics and it also provides powerful tools to application areas such as computer-aided geometric design, numerical analysis, and solutions of differential equations. q-Calculus is a generalization of many subjects, such as hypergeometric series, complex analysis, and particle physics. ¿¿This monograph is an introduction to combining approximation theory and q-Calculus with applications, by using well- known operators. The presentation is systematic and the authors include a brief summary.