Bose-Einstein condensation in a dilute weakly interacting atomic gas which happens at temperatures only millionth of a degree above absolute zero was first realized in 1995. Because of the deep connections with many important physics phenomena, such as superfluidity and superconductivity, it has since become one of most exciting subjects in physics, awarded by the Nobel Prize in 2001. But many intriguing problems in few-body and many-body physics arise when the particles of the dilute gas interact through strong long-range anisotropic forces, like the so-called polar molecules possessing a permanent electric dipole moment in their own frame. In the proposed joint experimental (CUHK) and theoretical (LAC) project COPOMOL, we will produce a quantum gas of polar 23Na87Rb bosonic molecules to study the ultracold physics with strong and anisotropic interactions, focusing on the precise control of ultracold molecule-molecule collisions with external electromagnetic fields to enter the regime where many-body physics is dominant. Inspired by the amazing achievements of the JILA group with 40K87Rb, we will take advantage of the remarkable properties of the 23Na87Rb ground state molecule, namely a large permanent dipole moment (5 times larger than in KRb) and a chemical stability against mutual collisions, to fully explore dipolar physics with quantum gases. The project will pursue the following objectives planned for the next four years: after the demonstration of the efficient production of Feshbach molecules, we will work out the best strategy for the reliable population transfer to the absolute molecular ground state with stimulated Raman adiabatic passage (STIRAP). Then the control of molecular collisions will be achieved by tuning of the anisotropic long-range dipole-dipole interactions with an external electric field, as a prerequisite to create a molecular quantum degenerate gas. Signatures of many-body physics phenomena in reduced geometries will be searched for by loading the quantum gas in an optical lattice. COPOMOL is timely given the particularly favorable configuration of the consortium. The CUHK group has already successfully prepared binary Na-Rb atomic BECs and investigated their interspecies Feshbach resonances. The LAC team includes several top experts on theoretical molecular structure, spectroscopy, and dynamics. Many high quality calculations related to heteronuclear alkali diatomic molecules, including NaRb, have been carried out while models for elastic, inelastic and reactive collisions between polar molecules have been developed. Another important fact is that the CUHK PI already has a long history of fruitful collaborations and discussions with the LAC PI and co-PI. Mastering these approaches is crucial as many applications proposed with dipolar interactions rely on the collisional properties of the ground-state molecules with and without induced dipole moment. The dangling question, whether trapped polar molecules without chemical reaction channels in the absolute lowest energy level will be really stable, will be answered first. We will measure and model the elastic and inelastic collisions with non-polarized and polarized samples to seek ways of achieving evaporative cooling for the production of a NaRb BEC. We will test the universal model for inelastic collisions with controlled loss channels including nuclear spin flips, rotational quenching, vibrational quenching and chemical reactions. These channels will be created by manipulating the internal state of the molecules with microwaves and lasers. These collisional studies will be further performed with molecules trapped in an optical lattice to explore the anisotropic character of dipolar interactions thus yielding a promising platform for observing several exotic many-body quantum phases.