Courant and Friedrich's classical treatise was first published in 1948 and tThe basic research for it took place during World War II. However, many aspects make the book just as interesting as a text and a reference today. It treats the dynamics of compressible fluids in mathematical form, and attempts to present a systematic theory of nonlinear wave propagation, particularly in relation to gas dynamics. Written in the form of an advanced textbook, it should appeal to engineers, physicists and mathematicians alike.

In 1981 I was approached by Klaus Peters to assist in publishing a selection of the papers of Kurt Otto Friedrichs. With some reluctance Friedrichs has agreed to help in making the selection although in the initial stages only one paper 47-2] was in his opinion worthy of being included. With some coaxing on my part the selection was made mainly by Friedrichs despite his frequent modest grumble that it did not make sense to include "that" paper as "X" had subsequently improved either the result or the proof. Later P.D. Lax and L. Nirenberg identified appropriate papers and, perhaps not so...

The work presented in this report originated in connection with a research project in magneto-hydrodynamics conducted by Professor H. Grad at the Institute of Mathematical Sciences at New York Univer- sity; the report was completed while the author was a consultant at Los Alamos Scientific Laboratory. The report contains an expository analysis of the mathematical structure of magneto-hydrodynamic theory; specifically, of the theory of the interaction of magnetic fields with conducting compressible fluids. One of the major aims is to emphasize the remarkably close parallelism between this...

In 1981 I was approached by Klaus Peters to assist in publishing a selection of the papers of Kurt Otto Friedrichs. With some reluctance Friedrichs has agreed to help in making the selection although in the initial stages only one paper 47-2] was in his opinion worthy of being included. With some coaxing on my part the selection was made mainly by Friedrichs despite his frequent modest grumble that it did not make sense to include "that" paper as "X" had subsequently improved either the result or the proof. Later P.O. Lax and L. Nirenberg identified appropriate papers and, perhaps not so...

The present lectures intend to provide an introduction to the spectral analysis of self-adjoint operators within the framework of Hilbert space theory. The guiding notion in this approach is that of spectral representation. At the same time the notion of function of an operator is emphasized. The formal aspects of these concepts are explained in the first two chapters. Only then is the notion of Hilbert space introduced. The following three chapters concern bounded, completely continuous, and non-bounded operators. Next, simple differential operators are treated as operators in Hilbert space,...