The book is a compendium of basic arguments of approximation theory, exposed in plain language and facilitating easy comprehension. The friendly exposition with the proper degree of deepening makes it a valid guide in master's degree courses or Ph.D. courses for students specializing in mathematics and also in applied mathematics fields. On the other hand, since it contains classical and also recent results on the approximation by polynomials, it is a valuable support in applied research activity based on global approximation methods. It consists of three chapters: (I) Approximation of Periodic Functions, (II) Algebraic Approximation on Unbounded Intervals and (III) Algebraic Approximation on Unbounded Intervals. [...]