We have great pleasure in presenting this text book of mathematics. This book is intended primarily for students of science and engineering. Its aims are, first, to present the fundamental mathematical ideas which underlie the notion of a convergent sequences, and secondly to develop, as far as the small spaces allows, a body of technique and a familiarity with particular examples sufficient to make the reader feel at home with such applications of infinite series as he is likely to meet in his scientific studies. Every topic has been explained in details and supported by a number of examples. This book is intended for students and researchers with a (special) interest in spaces of single and double sequences, matrix transformations and matrix domains.