This book describes a new concept of fine topological space. The collection of fine open sets contains all semi-open, pre-open, α-open,β-open etc. sets which are used in defining the lighter concepts of continuity. With this wider class of fine sets the authors have defined the continuity which includes several other continuities already defined. Csaszar A. has introduced the concept of generalized topological space in 2002. A fine topological space is a special case of generalized topological space, but it may be noted that the concept of fine space is based on a topological space. The notions of several continuous functions in topological spaces and fuzzy topological spaces are widely developed which are used extensively in many practical and engineering problems. The concept of continuity and homeomorphism are used in many fields such as in Chemistry, Computer Science, Physics, Zoology, Quantum physics, Quantum mechanics etc. Now, there is a wide scope of study this concept in view of fuzzy topological space.