Reddit mentions of An Introduction to Tensors and Group Theory for Physicists

J.F. Cornwell, Group theory in physics: an introduction (link)

W. Ludwig, Symmetries in physics: group theory applied to physical problems(link)

M. Tinkham, Group theory and quantum mechanics (link)

W.-K. Tung, Group theory in physics (link)

E.P. Wigner, Group theory and its applications to the quantum mechanics of atomic spectra (link1, link2)

N. Jeevanjee, An Introduction to Tensors and Group Theory for Physicists (link)

G. Costa, Symmetries and Group Theory in Particle Physics: An Introduction to Space-Time and Internal Symmetries (link)

B. Hall, Lie Groups, Lie Algebras, and Representations: An Elementary Introduction (link)

R. McWeeny, Symmetry: An Introduction to Group Theory and Its Applications (Dover Books on Physics)(link)

I recommend Tensors Demystified

Think of them as bras and kets. The downsies indices are bra like, they eat kets and spit out c-numbers. The upsies are ket like, they correspond to the original vector space. You can combine them to give two indices in the same manner as taking the tensor product of two or more kets to get the full state.

I found this book quite useful for an intro to group theory.

http://www.amazon.com/Introduction-Tensors-Group-Theory-Physicists/dp/0817647147/ref=sr_1_1?ie=UTF8&qid=1370289295&sr=8-1&keywords=jeevanjee

This one is probably the most intuitive description of tensors and group theory I've read, but it's not free =(