A new broadband two- and three-dimensional, polarization independent coordinate transformation is introduced that is capable of mapping the radiation from an embedded omnidirectional source into any desired number of highly directive beams pointed in arbitrary directions. This transformation requires anisotropic materials, yet is spatially invariant and thereby can be readily implemented by currently existing metamaterial technologies. Moreover, the performance of the transformation is not sensitive to small material parameter variations, thus enabling a broad operational bandwidth. To validate the concept, a broadband 3-D coordinate transformation metamaterial lens fed by a simple monopole antenna was designed, fabricated and characterized, achieving a quad-beam radiation pattern over a 1.26:1 bandwidth with approximately 6-dB realized gain improvement in the $H$-plane. In addition, the near-field coupling between the monopole and the lens was carefully tuned to accomplish a remarkable 70% broadening of the impedance bandwidth compared to the monopole antenna operating alone. It is also shown from the field simulations that the realized metamaterial lens provides both near-field and far-field 3-D collimating effects.