The Accelerator Collider Department (CAD) at Brookhaven National Laboratory is operating the Relativistic Heavy Ion Collider (RHIC), which includes the dual-ring, 3.834 km circumference superconducting collider and the venerable AGS as the last part of the RHIC injection chain. CAD is planning on a luminosity upgrade of the machine under the designation RHIC II. One important component of the RHIC II upgrade is electron cooling of RHIC gold ion beams. For this purpose, BNL and the Budker Institute of Nuclear Physics in Novosibirsk entered into a collaboration aimed initially at the development of the electron cooling conceptual design, resolution of technical issues, and finally extend the collaboration towards the construction and commissioning of the cooler. Many of the results presented in this paper are derived from the Electron Cooling for RHIC Design Report [1], produced by the, BINP team within the framework of this collaboration. BNL is also collaborating with Fermi National Laboratory, Thomas Jefferson National Accelerator Facility and the University of Indiana on various aspects of electron cooling.