Concerning the books by Carter, both have since been reprinted by Wiley in their "classics" series, though availability and cost right now is a serious question mark. The 1972 book is limited in scope, emphasizing Chevalley's 1955 approach to constructing simple groups (but over arbitrary fields). The 1985 book is considerably more expansive, emphasizing the Deligne-Lusztig characters and related matters about algebraic groups such as conjugacy classes. Two drawbacks: there are some mistakes (still uncorrected) and there is no treatment of the many further refinements by Lusztig and others. As Nick points out, Cedric Bonnafe's more recent Springer book on $SL_2$ over finite fields is well worth seeking out, in spite of its limited scope.

Anyway, the most recent MathSciNet reference for the 1985 book is here. Part of the problem with Carter's 1985 book is that he himself left mathematics some years ago and is now quite elderly. But the book does have a lot of detailed information which is not readily found elsewhere. It's a subject which deserves a fresh textbook treatment. Good luck.

ADDED: Maybe it's worthwhile to point out that Geck and Malle are in the process of writing a book of their own about the characters of the finite groups of Lie type: see their preprint of Chapter 1.

Concerning the books by Carter, both have since been reprinted by Wiley in their "classics" series, though availability and cost right now is a serious question mark. The 1972 book is limited in scope, emphasizing Chevalley's 1955 approach to constructing simple groups (but over arbitrary fields). The 1985 book is considerably more expansive, emphasizing the Deligne-Lusztig characters and related matters about algebraic groups such as conjugacy classes. Two drawbacks: there are some mistakes (still uncorrected) and there is no treatment of the many further refinements by Lusztig and others. As Nick points out, Cedric Bonnafe's more recent Springer book on $SL_2$ over finite fields is well worth seeking out, in spite of its limited scope.

Anyway, the most recent MathSciNet reference for the 1985 book is here. Part of the problem with Carter's 1985 book is that he himself left mathematics some years ago and is now quite elderly. But the book does have a lot of detailed information which is not readily found elsewhere. It's a subject which deserves a fresh textbook treatment. Good luck.

ADDED: Maybe it's worthwhile to point out that Geck and Malle are in the process of writing a book of their own about the characters of the finite groups of Lie type: see their preprint of Chapter 1.

Concerning the books by Carter, both have since been reprinted by Wiley in their "classics" series, though availability and cost right now is a serious question mark. The 1972 book is limited in scope, emphasizing Chevalley's 1955 approach to constructing simple groups (but over arbitrary fields). The 1985 book is considerably more expansive, emphasizing the Deligne-Lusztig characters and related matters about algebraic groups such as conjugacy classes. Two drawbacks: there are some mistakes (still uncorrected) and there is no treatment of the many further refinements by Lusztig and others. As Nick points out, Cedric Bonnafe's more recent Springer book on $SL_2$ over finite fields is well worth seeking out, in spite of its limited scope.

Anyway, the most recent MathSciNet reference for the 1985 book is here. Part of the problem with Carter's 1985 book is that he himself left mathematics some years ago and is now quite elderly. But the book does have a lot of detailed information which is not readily found elsewhere. It's a subject which deserves a fresh textbook treatment. Good luck.

Concerning the books by Carter, both have since been reprinted by Wiley in their "classics" series, though availability and cost right now is a serious question mark. The 1972 book is limited in scope, emphasizing Chevalley's 1955 approach to constructing simple groups (but over arbitrary fields). The 1985 book is considerably more expansive, emphasizing the Deligne-Lusztig characters and related matters about algebraic groups such as conjugacy classes. Two drawbacks: there are some mistakes (still uncorrected) and there is no treatment of the many further refinements by Lusztig and others. As Nick points out, Cedric Bonnafe's more recent Springer book on $SL_2$ over finite fields is well worth seeking out, in spite of its limited scope.

Anyway, the most recent MathSciNet reference for the 1985 book is here. Part of the problem with Carter's 1985 book is that he himself left mathematics some years ago and is now quite elderly. But the book does have a lot of detailed information which is not readily found elsewhere. It's a subject which deserves a fresh textbook treatment. Good luck.

ADDED: Maybe it's worthwhile to point out that Geck and Malle are in the process of writing a book of their own about the characters of the finite groups of Lie type: see their preprint of Chapter 1.