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I'm a Physics student and I'm planning to go to grad school in theoretical physics (I'm still in my first year so things may change but oh well) My question is twofold:

1. Any good book on Lie group and its application to physics, for someone with no formal course in group theory (Something that could build group theory up to Lie theory would be perfect!)?

2. A book on functional analysis, with application to Fourier Analysis and Probability (preferably).

My background is : Complex Analysis at the level of Stein, Measure Theory at the level of Halmos, Differential geometry at the level of Docarmo and Manifold Theory at the level of Boothby.