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''.