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Group Theory and Physics, by S. Weigert (1990) World Scientific.This book is too technical for physicists, but nevertheless, I've found it useful for group theory. The physics approach isn't always clear, but the mathematics is. The first edition of this book is out of print, but it's still worth looking up from time to time.

Lie Groups: Differential Geometry, Lie Algebras, and Applications, by K. Yano, S. Ishihara, B. O�Freed and F. Gherardelli (1990) Springer.Is mainly about differential geometry of Lie groups, and has a good section on how to use the Lie theory in physics.

Beware of other books which focus on Lie groups, like Ravinder, but who don't know any of the standard physics terminology or applications. That unfortunately means they'll teach you what a Lie group is, instead of how to use it. In that regard, the first edition of the GTB is one of the best I've ever seen.

Lie Groups : An Approach through Invariants and Representations, by R.W. Lawther, H. W. Gould (1990) Springer.Has a somewhat mathematical approach. From the preface, I gather it's meant for people familiar with invariant theory, like physicists, but it could be useful for more mathematics-inclined readers who need a quick intro to Lie groups.

Lie Groups: An Introduction, by F. Gliozzi, R. Mezzidi, P. Tempesta (2016) Springer.Is written for mathematicians, and has a good treatment of Lie groups, although it's sometimes not very clear when the group is Lie vs non-Lie. Still, it's a good starting point.

In my own attempt to bring the application of group theory to physics, I have tried to keep as close to mainstream physics as possible - I've written up the notation and presentation of group theory in the language of Lie's Algebra and Lie Groups. This has the advantage that it's essentially self-contained, so you don't need to know how Lie groups are constructed to understand it. It's also strongly based on physics notations and assumptions and is in some ways a complete re-writing of some of the mathematics that's been done over the years in the equivalent physics communities, so that you don't need to go back to the literature to find the answers, you can simply read them out of the paper. (Even in the original papers, the physicists usually talk about Lie groups in the more general Lie algebraic context. The physicists are mainly interested in the representations and symmetry breaking of Lie groups, but Lie algebras are a useful mathematical tool to get them to do so).

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