The book considers properties of polynomial, exponential, logarithmic and power functions. It introduces and proves important relationships between these functions, which enhances the theory and greatly improves the range of theoretical and practical applications, such as the modeling of physical, societal or economical processes. Relationship of the considered functions with the physical reality is another primarily subject of this book. Lots of illustrations and examples based on physical, biological, societal phenomena constitute a substantial part of the book, that facilitates the understanding of introduced modeling concepts and methods. The book is an excellent supplementary material for mathematical and physical courses for undergraduate and graduate studies; a valuable resource for mathematicians working in areas of algebra and analysis. Engineers, researchers, analysts, who use these functions in modeling of different processes and phenomena, will greatly benefit from this book.