A Course on Topological Groups (Texts and Readings in Mathematics) Paperback – 30 July 2011

This is a good text for understanding some important theorems in topological groups but isn't a complete source

If you are really interested about Topological group, I would suggest you to go for "Profinite group" by wilson. In this book, it is assumed that the Topological space is T_1 and also only first chapter is about topological group...as the motive of the book is a particular theorem that author mention at preface. So, read wilson book for better understanding the general situation....

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Good one