This book describes concept of generalized continuity and generalized separation axioms in fine topological space. The collection of fine-open sets contains all semi-open pre-open α-open β-open etc. sets which are used to define the generalized concepts of continuity which includes several continuities already defined. The fine-topological space is a special class of generalized topological space which is based on a topological space. The concept of continuity and homeomorphism are used in many fields such as in Quantum physics Quantum mechanics computer science chemistry physics etc.