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The book comprises of eight chapters.Chapter 1 we present conceptual framework which will be needed in the sequel.Chapter 2 we introduce the notion of Nb-cone metric space over Banach algebra and establish some topological properties. We also prove some coupled fixed-point results.Chapter 3 we derive some coupled common fixed point results in Nb-cone metric space over Banach algebra.In Chapter 4, we define the notion of Np-cone metric spaces over Banach algebra as a generalization of N-cone metric spaces over Banach algebra.Chapter 5 deals with introducing the notion of F-cone metric spaces over Banach algebra as a generalization of Nb-cone metric space over Banach algebra and Np-cone metric space over Banach algebra.The purpose of this Chapter 6 is to introduce a new generalization of the b-metric-like spaces called cone b-metric-like space over a Banach algebra.Chapter 7 is devoted to introduce the notion of A-cone metric spaces over Banach algebra as a generalization of A-metric spaces and cone metric spaces over Banach algebra.In chapter 8 we establish a new space called partial cone b-metric space by using both the notions of cone b-metric spaces and partial metric spaces.