Some problems in mathematical analysis (e.g., in theory of function spaces, in approximation theory or in interpolation theory) lead to the investigation of weighted inequalities on certain classes of quasiconcave functions on the interval I=(a,b) R. In this book we analyse the class Q (I) of -quasiconcave functions in a complete generality in order to establish results needed for a comprehensive study of weighted inequalities on the class Q (I). We illustrate our results on weighted inequalities of Hardy type, on weighted inequalities of Hardy type involving supremum, and on reverse forms of these inequalities.