The star transform is a generalized Radon transform mapping a function of two
variables to its integrals along "star-shaped" trajectories, which consist of a
finite number of rays emanating from a common vertex. Such operators appear in
mathematical models of various imaging modalities based on scattering of
elementary particles. The paper presents a comprehensive study of the inversion
of the star transform. We describe the necessary and sufficient conditions for
invertibility of the star transform, introduce a new inversion formula and
discuss its stability properties. As an unexpected bonus of our approach, we
prove a conjecture from algebraic geometry about the zero sets of elementary
symmetric polynomials
