I am looking for a good book on Topological Groups. I have read Pontryagin myself, and I looked some other in the library but they all seem to go in length into some esoteric topics.


I would love something 250 pages or so long, with good exercises, accessible to a 1st PhD student with background in Algebra, i.e. with an introduction covering necessary background in Functional Analysis.


If possible, I would also like it covering particularly important (in my view) topics:


* emphasize on locally compact groups, but both locally Euclidean and totally disconnected cases;
* [Pontryagin duality](https://en.wikipedia.org/wiki/Pontryagin_duality);
* [Kazhdan property T](https://en.wikipedia.org/wiki/Kazhdan%27s_property_(T));
* [Tannaka reconstruction](https://en.wikipedia.org/wiki/Tannaka%E2%80%93Krein_duality#Theorems_of_Tannaka_and_Krein).



What is a good book on topological groups?
I'm not aware of a book that covers simultaneously Pontryagin duality, property (T) and Tannaka duality. I will refrain from recommending any book on property (T) (guess why?). Apart from Weil's book already mentioned, my favourite ones are:


* for Pontryagin duality: Rudin's "Fourier analysis on groups";
* for functional analytic aspects: Loomis' ``An introduction to abstract harmonic analysis'';
* for representation theory and Tannaka duality (and learning through exercises!): Kirillov's ``Elements of the theory of representations''.
* for group $C^\*$-algebras: the second half of Dixmier's $C^\*$-algebras''.


