Properties of the ray transforms of two-dimensional $2$-tensor fields given in the unit disk

We study the longitudinal, transverse, and mixed ray transforms acting on two-dimensional symmetric $2$-tensor fields. Namely, the kernels of the ray transforms are described; the connection between the ray transforms and the Radon transform is established; unconditional estimates of stability for each of the ray transforms are obtained; inversion formulas for a recovery of symmetric $2$-tensor field components and for a recovery of the potential are obtained; projection theorems for the ray transforms are proved.