An Introduction to Tensors and Group Theory for Physicists
During my years of studying mathematical physics I spent much time trying to connect the rigorous but abstract mathematics found in pure math texts with the hands-on but fuzzy treatment of that same mathematics in physics texts. This book is the result of that process. The first edition came out in 2011, and the second in 2015. A partial solution set has also been posted (see below).
(Note: for additional reviews on Amazon, see the 1st edition Amazon page linked below.)
Reviews: Physics Today MAA MathSciNet Amazon(1st edition)Purchase: Amazon(2nd edition)     Springer Errata: 1st edition 2nd edition Solutions: 2nd edition