When I was a student, I studied the subject using a very old book "Topological groups", written by L. S. Pontryagin. It was in Russian, but Google search shows that there is a translation in English.

Thank you sir

I just got this through online. I think this book will help me a lot. Thank you very much sir.

Sir,

TOPOLOGY, by James R Munkres

The most important topological groups are Lie Groups. I would start with them and then generalize. There is a text book which introduces Lie Group using matrixes as examples:-- "Lie Groups: A problem-Oriented Introduction via Matrix Groups" by Harriet Pollatsek. Note that you will see Lie Algebras also discussed with Lie Groups, but this association does not generalize to topological groups.

An Introduction to Topological Groups by P. J. Higgins

• Alexander Arhangel’skii
• Mikhail Tkachenko

Topological Groups and Related Structures Book Topological Groups and Related Structures

I would recommend a very recent, carefully written informative and friendly book

"Topological Groups and the Pontryagin-van Kampen Duality: An Introduction" by Lydia Außenhofer, Dikran Dikranjan, Anna Giordano Bruno

Book Topological Groups and the Pontryagin-van Kampen Duality: An...

https://link.springer.com/content/pdf/bbm%3A978-94-91216-35-0%2F1.pdf