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;
- Kazhdan property T;
- Tannaka reconstruction.

andcovering all those topics, while including an "introduction covering necessary background in Functional Analysis"?Really? $\endgroup$