The recent development in quantum field theory has led physicists to consider the so-called super theories. Physically, super theories emerged from the attempt to create appropriate counterparts of Fermions, whereas the mathematical framework focuses on the study of geometric objects associated with super commutative rings, together with the representations of their cohomological invariants in derived categories. The significance of super theories in physics has gained increasing evidence, to a large extent, by the epoch-making ideas and arguments of E. Witten. As for the mathematical framework of super (algebraic) geometry, the monography of \textit{Yu. I. Manin} on ``Gauge field theory and complex geometry'' (Moskau 1984; Zbl 0576.53002; English translation: 1988) is among the most valuable sources. In 1988, \textit{N. Kawamoto}, \textit{Y. Namikawa}, \textit{A. Tsuchiya} and \textit{Y. Yamada} gave a geometric realization of a conformal quantum field theory on so-called Virasoro uniformized Riemann surfaces [cf. Commun. Math. Phys. 116, No. 2, 247-308 (1988; Zbl 0648.35080)]. In their theory, the description of the moduli space of those Virasoro uniformized Riemann surfaces is of crucial importance, and this is basically achieved by using its embedding in Sato's universal Grassmann manifold and a suitable generalization of Hirota's tau function. This approach, in the non-super case, is the starting point of the present paper. The author's aim is to develop an analogous theory within the framework of (infinite-dimensional) super algebraic geometry. Based on the concept of an affine super scheme associated with a super commutative ring, the author introduces the notion of a ``family of Virasoro uniformized (compact) super Riemann surfaces'', and these super objects are then discussed extensively in the course of the paper. The author's main goal is to classify Virasoro uniformized super Riemann surfaces by the coefficients of a suitable analogue of the non-super tau function, or (equivalently) by suitable super versions of the classical theta functions of Jacobians of compact Riemann surfaces. This strategy is realized by constructing a ``super tau function'' as an infinite Beresinian (i.e., as a super determinant of an infinite matrix) and, in the sequel, by interpreting it as a sort of ``super theta function''. To this end, the concept of a ``super Jacobian'' (as a moduli space of line bundles on a super Riemann surface) is introduced, and then the super tau function is interpreted as a section of a line bundle over the super Jacobian. At the end of the paper, the super tau function (or super theta function, respectively) is further analyzed by complex-analytic methods, and this is the concluding step for proving the main results on the super tau function mentioned above. The paper is written in an extremely careful, thorough and clear style. The construction of the super tau function (and the super theta function) is a highly important and welcome contribution to the development of super geometry and its applications in quantum field theory. -- As the author mentions in the preface of his paper, another theory of a super tau function calculus has been constructed by \textit{A. S. Schwarz} in 1989 [cf. ``Fermionic string and universal moduli space,'' Nuclear Physics, Particle Physics, B 317, No. 2, 323-343 (1989)]. The approach worked out in the present paper, however, seems to be more geometrical and, therefore, more convenient for the purpose of using the super tau function in the study of moduli spaces of line bundles over super Riemann surfaces.