The subject of this work are double sequences and double series. In the first chapter we present some basic results on double sequences related to convergence, monotonicity and bimonotonicity. Double series and their convergence is considered in the second chapter. In Section 2.1, the convergence of geometric, exponential, harmonic double series and its variants is discussed. We relate the convergence of a double series to the convergence of the corresponding iterated series (Fubini’s theorem, Tonelli’s theorem). In Section 2.4, we introduce the concept of absolute and conditional convergence of a double series, and obtain some useful characterizations of absolute convergence. Various tests for determining absolute and conditional convergence of a double series are given in Section 2.6. Double power series are considered in Section 2.7. A double power series may have many biradii of convergence. Also, its domain of convergence can have a variety of shapes, and it need not even be a convex subset of R2. In Section 2.8, Taylor double series is treated as a special case of a double power series. The corresponding diagonal series, called the Taylor series, is considered as well.