  A Radon-type transform called a cone transform that assigns to a given
function its integral over various sets of cones has arisen in the last decade
in the context of the study of Compton cameras used in Single Photon Emission
Computed Tomography. Here, we study the cone transform for which the central
axis of the cones of integration is fixed. We present many of its properties,
such as two inversion formulas, a stability estimate, and uniqueness and
reconstruction for a local data problem.
