Here are 10 things to know:
The Sensex ended 376.60 points - or 0.94 per cent - higher at 40,522.10 and the Nifty settled at 11,889.40, up 121.65 points - or 1.03 per cent - from its previous close.
Kotak Mahindra Bank, Nestle, Asian Paints, Shree Cement and Bajaj Finance, ending between 4.38 per cent and 11.70 per cent higher, jumped the most among 32 gainers in the 50-scrip index. On the other hand, HDFC, Tata Consultancy Services, ONGC, Infosys and Wipro, down 1.46-2.10 per cent each, were the top Nifty losers.
Kotak Mahindra Bank, HDFC Bank and Asian Paints were the biggest boosts to Sensex, together contributing more than 300 points to the gain in the index.
Kotak Mahindra Bank shares 11.86 per cent higher at Rs 1,583.60 apiece on the BSE, a day after the lender reported a 27 per cent increase in its net profit to Rs 2,184.48 crore in the July-September period. The bank's profit beat analysts' expectations, according to news agency Reuters. The stock was the top gainer in both indices.
The Nifty Bank index - which tracks stocks of 12 major lenders - closed 2.88 per cent higher. Besides Kotak, other prominent gainers included Axis Bank, HDFC Bank and ICICI Bank, each ending 1.45-2.81 per cent higher.
Bharti Airtel and Tata Motors will report their earnings for the quarter ended September 30 later in the day.
MSCI said on Monday it would will implement changes in foreign ownership limits (FOL) in its global indices containing Indian securities in November.
The expectation of higher foreign inflows following MSCI's index recast is keeping markets away from a free fall, said Anand James, chief market strategist at Geojit Financial Services.
Sentiment in other Asian markets was weak as concerns grew over a second wave of coronavirus infections in the US and Europe, sending MSCI's gauge of Asia-Pacific stocks outside Japan down 0.43 per cent.
European share markets started the day on a negative note, with the United Kingdom's FTSE 100 index trading 0.58 per cent lower in early deals. The Eurostoxx 50 benchmark index was down 0.60 per cent.