Hello,
The Indian Institute of Science, or IISc, was founded in 1909 and designated as a deemed university in 1958. However, the undergraduate programme (Bachelor's degree) began in 2011. The first IISER, on the other hand, did not appear until 2006. All of these institutes have the goal of promoting advanced scientific and technical research and education in India (as stated on the website).
Now, if the criterion is any national rankings list, IISc is at the top of it or at least ranks higher than IISER, Pune, which is generally the top IISER. To begin with, don't ask me how Engineering and Science institutes are included together in a single survey and list; I, too, am looking for solutions to such issues. Second, IISc is a well-known and respected institution.
IISc has a large alumni base, with many people achieving great success in their chosen professions. Because IISERs are younger institutes, their alumni networks aren't as strong as the IISc's, but they're not awful either. And believe me when I say that this scenario for the IISERs is set to alter dramatically in the next years.
To summarise, IISc is undoubtedly the finest, but IISERs are also excellent. If you want to pursue a career in research, any of these institutes will provide you with a solid foundation. I hope this information is useful.
All the best!!
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