The term sequence has a great role in real Analysis. The generalized notion of single sequences are the double sequences. Every double sequence is an infinite matrix. various types of linear spaces of double sequences are constucted and studied their properties. The difference operator is used on the double sequences to construct a new double sequence. The double sequences may be bounded, unbounded, convergent, non-convergent or some other. Depending on the behaviour of the sequences the sequence spaces are constructed and some properties of functional analysis are established. The book intends the role of infinite matrices to construct sequence spaces. Efforts have been done for the readers belonging to Analysis, Linear algebra and functional analysis. The studies on double sequence spaces are new in functional analysis. A few works have been done on the studies of difference double sequence spaces. Hope that readers will be benefited for introducing new ideas from this book. A complete development on the studies of double sequences and difference operator is depicted in the first chapter of the book. In the remaining two chapters some new results are added.

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