A topological space can be thought of as a set form which has been swept away all structure irrelevant to the continuity. So, concepts of semi-continuity, weaker-continuity and pre-continuity are widely acceptable in topological domain. This book imparts latest developments in various forms of continuity in a topological space and their classifications, decomposition and successful applications. The book is aimed at providing conceptual skill in various forms of continuity in topological space, which is very needful for researcher of spatial and topological object modeling and students of advance algebraic topology.