Prime Minister Narendra Modi chose climate change, infrastructure and sustainable development as the BRICS summit's main goals. India's USD 2.38 trillion economy is growing 7.5 percent annually, fastest of the five countries.
At a summit this weekend, the BRICS nations - Brazil, Russia, India, China and South Africa - will be looking for ways to boost trade between their developing economies, representing nearly half of the world's population.
Latin America's largest economy, at USD 1.35 trillion, is forecast to contract about 3 percent this year after an equally dismal 2015. Unemployment and inflation are both hovering around 10 percent. Some states including Rio de Janeiro are so broke they haven't paid public workers in months.
Brazil's recovery is crucial to South America's economic future. But the country of 206 million people relies heavily on prices of oil, soy and other commodities, which have plunged.
Since taking over the national leadership from Dilma Rousseff, after she was removed amid allegations of misusing funds, President Michel Temer has made changes that already are cheering markets: The real has started strengthening against the dollar, after plunging in recent years. But the reforms are deeply unpopular, especially among those who have lost their jobs.
In Goa, Brazil is looking to boost business for its IT and pharmaceutical industries, and to help its energy, sanitation and all-important farming sectors.
As tensions with the US have escalated, Russia has wooed China. Moscow was the only government to speak on China's behalf after an arbitration panel in The Hague ruled against Chinese claims to nearly all disputed South China Sea territories.
Russia's courtship of China follows Western sanctions and an oil price slump that hit its USD 1.13 trillion economy hard. Last year, Russia's GDP shrank 3.7 percent before stabilizing as energy markets rebounded. It remains weak, however, with the International Monetary Fund predicting a further contraction of 0.8 percent this year and modest growth in 2017.
Putin is due to meet with India's Prime Minister Narendra Modi on the sidelines of the BRICS summit on Saturday, where they are expected to discuss Syria and Afghanistan. The two also aim to expand nuclear ties, with Russia building several reactors in India. After decades of close Cold War-era relations between New Delhi and Moscow, Russia has been unnerved by Modi's effort to build closer economic and defense ties with Washington.
Bilateral trade fell more than 14 percent from USD 10 billion in 2014, a decline Russia has blamed on the global oil market turmoil.
India also expressed annoyance with Russia's recent joint military exercises with Pakistan, which India says "sponsors and practices terrorism as a matter of state policy," Press Trust of India news agency quoted Indian Ambassador Pankaj Saran as saying in Moscow.
Prime Minister Narendra Modi chose climate change, infrastructure and sustainable development as the BRICS summit's main goals. India's USD 2.38 trillion economy is growing 7.5 percent annually, fastest of the five countries. But it also has the world's highest number of people in poverty, with more than half of its 1.3 billion population living on less than USD 3.10 a day.
Indian government advisers have set up three working groups at the summit focused on counter-terrorism, cyber-security and energy security, according to Foreign Ministry official Amar Sinha.
India also wants to launch a BRICS social services agreement, financial services framework and possibly a think tank.
But Modi is also expected to seek support for India against Pakistan's alleged backing of separatist rebels in the conflict-ridden Himalayan region of Kashmir. Daily protests and rebel attacks have dominated Indian news in recent months, and at least 80 civilians have been killed in clashes with law enforcement.
China is unlikely to support any statement criticizing its close ally Pakistan.
China's economy is growing at its slowest pace in 25 years, but it is the world's second largest after the US at USD 11.4 trillion.
President Xi Jinping is likely to be looking to expand access for Chinese goods to foreign markets. On Thursday, Chinese state media argued strongly for the BRICS to adopt a free-trade agreement. While the Chinese government has made no such proposal formally, its Commerce Ministry has said it is keen on the idea.
The other BRICS, already burdened by cheap Chinese imports and huge trade deficits with Beijing, are likely to balk.
China, a nation of 1.38 billion people, will also likely be seeking support in Goa for a proposed trade route through Central Asia and Russia to Europe, and for a sea route traversing the Indian Ocean. Chinese Foreign Minister Li Baodong this week called that "One Belt, One Road" initiative a national priority.
Xi may try to seek Indian support for the trade route initiative in exchange for backing India's bid to join the Nuclear Suppliers Group, a grouping of 48 countries that have agreed to adhere to guidelines for nuclear and nuclear-related trade meant to prevent the spread of nuclear weapons.
With its credit rating hovering near junk status in recent months, South Africa's stumbling economy is headed for more trouble as the country's finance minister answers charges of fraud and its currency remains unstable.
The country's finance ministry has said the legal proceedings will damage "the economic well-being of South Africans and essential processes of government."
South Africa's economy, by far the smallest among the BRICS, was estimated at USD 327 billion in 2015, while unemployment among its population of 55 million is at a daunting rate of about 23 percent.
Still, South Africa's vast mineral wealth makes it a valuable ally to the other major developing nations.
There has been little word of what its president, Jacob Zuma, may be hoping for from the summit.