The purpose of these notes would have been better explained if we had chosen another title， namely， Jacquet-Langlands' Theory Made Easy； it occurred to us at the last moment that a more pedestrian choice would be more prudent， since after all the author is in a rather bad position to judge.These notes cover a very large part of Chapters 2， 3， 5， 6， 9， 10 and 11 of Jacquet-Langlands' work， Automorphic Forms on GL（2）， VII 548 pp.， 1970， Springer （Lecture Notes in Mathematics， No. 114）. Since the volume of our notes is about one fifth of 548 pp.， it is not to be expected that we have been able here to explain everything. In fact， we have entirely omitted the explicit construction of discrete series from quadratic extensions or quaternion algebra （Chapter 4 of Jacquet and Langlands）， the connection with Zeta functions of matrix algebras （Chapter 13）， and the most interesting， or at any rate newest， part of their work， namely， the relations between the "spectra" of a quaternion algebra and a 2×2 matrix algebra...
