I teach a course on group theory for physics at the level of senior undergraduates. I follow basically the book by Georgi "Lie algebra in particle physics". So I teach them, the groups SU(2), SU(3) and other related subjects. However there are too little exercises in this book, and I couldn't find enough exercises on the net. Do you know where can I find exercises on group theory FOR physicists?
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I can recommend H.F. Jones, ``Groups, representations and physics'', Institute of Physics Publishing, 1990: it has a good selection of exercises at the end of each chapter. 


WuKi Tung's Group Theory in Physics has problems at the end of each chapter. Michael Aizazis published the complete solutions to these problems. 


I think that the H.F. Jones book "Group Theory in physics" can be another good reference. 

