Sagan's book on the symmetric group is a great introduction to algebraic combinatorics, tracing the combinatorial approach to understanding the representation t

Sagan's book on the symmetric group is a great introduction to algebraic combinatorics, tracing the combinatorial approach to understanding the representation theory of the symmetric group. For more depth in that direction, Fulton & Harris' 'Representation Theory' builds the connections with Lie groups. Algebraic combinatorics dances in the intersection of a number of fields of mathematics, where some of the most fundamental and beautiful structures are to be found. I had a relatively large breadth of knowledge coming out of my phd as a result, which I'm pretty happy about.