This short book is patterned very much on the classical books by Knapp and by Bromwich. The book is self-contained and deals with most of the standard topics covered in a detailed course in infinite series. Chapter headings are the following: Infinite sequences, Infinite series: series of positive terms, Series in general, Derangement of series, Double series, Multiplication of series, Uniform convergence, Real power series, Infinite products, Tannery's theorems, Complex series and products, Transformation into a more rapidly convergent series and Summability processes. While the earlier parts of the book contain exercises which are within the reach of a student, the later ones have few or at times none. The virtue of the book is that it contains the standard material presented clearly with mathematical rigor and as such has strong claims for adoption as a text-book.