In this book, the author has introduced and studied the concepts of intuitionistic Smarandache topological semigroups, intuitionistic Smarandache topological semigroup structure spaces, intuitionistic SG exterior spaces, intuitionistic t-open sets, intuitionistic t continuous functions, intuitionistic t-kernel sets, intuitionistic t-kernel Hausdorff spaces, intuitionistic weak sieve structure spaces, intuitionistic weak sieve t-open sets, intuitionistic weak sieve t-continuous functions, intuitionistic weak sieve feebly t continuous functions, intuitionistic weak sieve t-compactly generated spaces, intuitionistic weak sieve t-locally compact spaces, intuitionistic F_structure spaces, intuitionistic F_ feebly normal spaces, intuitionistic F* nearly compact spaces, intuitionistic Fc* door spaces, intuitionistic Fc*irreducible spaces, intuitionistic monoid structure spaces, intuitionistic monoid connected spaces, intuitionistic monoid totally semi-continuous functions, intuitionistic Ms Noetherian spaces. Some interesting properties, characterizations & interrelations among the concepts are established.