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The book consists of 9 chapters.Chapter 1 The first chapter presents some preliminaries and historical notes on metric spaces.Chapter 2 We study asymptotically regular maps and sequences in partial cone metric spaces and derive some fixed point results.Chapter 3 We aim to deal with expansive maps in Partial cone metric spaces and prove some results.In Chapter 4 we discuss the notion of the N-cone metric spaces, define asymptotically regular maps and prove some fixed point theorems.In Chapter 5 we define topology and prove unique fixed point theorems for contractive maps in N-cone metric spaces.Chapter 6 is devoted to introducing the notion of N-fuzzy metric spaces, described some properties and also proved some fixed point theorems.In Chapter 7 we introduce a new space called Nb-cone metric space. We define expansive mapping for the new setting and prove some fixed point theorems.In Chapter 8 we introduce pseudo-G-metric spaces and pseudo-G-metric product spaces.Chapter 9 is devoted to another new space named Cone metric-like space over Banach algebra. We define Generalized Lipschitz map and proved some fixed point results.