Chennai Mathematical institute (CMI) tops the list followed by IMSc and IISc.
Tata Institute of Fundamental Research(TIFR),
Harishchandra Research Institute(HRI),
Indian Statistical Institute (ISI Kolkata & Delhi)
University of Hyderabad,
BITS Pilani,
Institute of Chemical Technology (ICT, BOMBAY) for Engineering Mathematics
and then IITs join the list,
IIT DELHI, IIT MADRAS, IIT KHARAGPUR, IIT BOMBAY, IIT GUWAHATI and IIT ROORKEE.
Though IITs are considered to be the heaven of engineers but talking in the term of Mathematical advances and exploration, above mentioned institutes are leading the generation.

BHU (Banaras Hindu University)
Central University of Kerala
Central University of Karnataka
University of Hyderabad
Anna University is also considered best for MSc Mathematics as well as MSc Applied Mathematics.
Jadavpur University in West Bengal is also good. It stands at no. 5 as per NIRF 2017 Ranking.
NIT WARANGAL
NIT TRICHY
NIT CALICUT are the best institutes to study Mathematics in India.