The object is to provide a mask blank substrate, a mask blank, and a transfer mask which can achieve easy correction of a wavefront by a wavefront correction function of an exposure apparatus. The further object is to provide methods for manufacturing them.A virtual surface shape, which is an optically effective flat reference surface shape defined by a Zernike polynomial, is determined, wherein the Zernike polynomial is composed of only terms in which the order of variables related to a radius is second or lower order and includes one or more terms in which the order of the variables related to a radius is second-order; and the mask blank substrate, in which difference data (PV value) between the maximum value and the minimum value of difference shape between a virtual surface shape and a composite surface shape obtained by composing respective surface shapes of two main surfaces is 25 nm or less, is selected.