This invention concerns a biopolymer consisting of a polysaccharide composed of galactose (50-90%), glucose (1-25%), mannose (1-25%) and rhamnose (0.5-20%), which may additionally contain, in trace amounts, xylose, fucose, ribose, arabinose and/or fructose. The galactose-rich polymer also contains non-saccharide components, namely, acyl groups. This invention also concerns a process for the production of the galactose-rich polymer, by microbial fermentation using glycerol or glycerol-rich substrates as carbon source, and recovery of the polymer from the culture broth. From the process for the production of the galactose-rich polymer results the co-production of intracellular biopolymers, namely, polyhydroxyalkanoates. This invention also concerns to the application of the galactose-rich polymer and the products of its partial or complete degradation and/or derivatization, namely, galacto-oligosaccharides, galactose, rhamnose and others, by physical, chemical and/or biological methods, in food, agricultural, textile and paper industries, pharmaceutical and cosmetic products, oil and metal recovery in mining industry, industrial waste treatment and wastewater treatment, among others.