SL2(R) gives the student an introduction to the infinite dimensional representation theory of semisimple Lie groups by concentrating on one example - SL2(R). This field is of interest not only for its own sake, but for its connections with other areas such as number theory, as brought out, for example, in the work of Langlands. The rapid development of representation theory over the past 40 years has made it increasingly difficult for a student to enter the field. This book makes the theory accessible to a wide audience, its only prerequisites being a knowledge of real analysis, and some differential equations.

Serge Lang (May 19, 1927 – September 12, 2005) was a French-born American mathematician. He is known for his work in number theory and for his mathematics textbooks, including the influential Algebra. He was a member of the Bourbaki group.

Lang was born in Paris in 1927, and moved with his family to California as a teenager, where he graduated in 1943 from Beverly Hills High School. He subsequently graduated from the California Institute of Technology in 1946, and received a doctorate from Princeton University in 1951. He held faculty positions at the University of Chicago and Columbia University (from 1955, leaving in 1971 in a dispute). At the time of his death he was professor emeritus of mathematics at Yale University.