I know a bit.
Their capital was at Palembang, and that was an extremely important centre of trade. They had good relations with China, and extended their power over Java and the Malay peninsula.
They were Buddhist (Hindu?? - not sure), and their first fall came when some Javans torched Palembang in the 9th (not sure) century. They recovered, but were ultimately beaten by the Hindu Majapahits of Java in 1200 or something.
They had sent a diplomat to China asking for vassalisation (to save them from the Javans0, and the Chinese agreed, thinking the situation the same until some diplomats were killed by Javans. Thus ended Sri Vijaya.
Their monatch fled to Singapore, then to Melaka: Voila! Melaka was formed, and tried to mirror the greatness of Sri Vijaya. Sri Vijaya was so respected that Melaka was respected as much, for they were related from Sri Vijaya.