For physics students interested in the mathematics they use, and for math students interested in seeing how some of the ideas of their discipline find realization in an applied setting. The presentation strikes a balance between formalism and application, between abstract and concrete. The interconnections among the various topics are clarified both by the use of vector spaces as a central unifying theme, recurring throughout the book, and by putting ideas into their historical context. Enough of the essential formalism is included to make the presentation self-contained.
I've read some parts of this book. It is more like mathematics books. Sometimes there are many definitions and developments of the subjects which are unnecessary for physicists. However, if a physicist likes or needs abstract and solid foundation of a the mathematics he or she uses, then this book is absolutely useful.