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I would like to ask if somebody is aware of a textbook or internet lecture notes on Lie groups which are accessible for someone with solid background in (general) group theory and topology, but who is not so strong in differential geometry.

My main background is in functional analysis, but I believe I have a reasonable knowledge of group theory (including topological groups) and of (algebraic and general) topology, but quite limited knowledge of differential geometry. So I would prefere a book which introduces differential geometric concepts as needed during the course.

I am now studying (general infinite-dimensional) unitary representations of locally compact groups, but without reasonable understanding of Lie groups I feel half blind.

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John Stillwell's Naive Lie theory is what you are after.

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