This comprehensive and long-awaited volume provides an up-to-date account of those parts of the theory of bounded and closed linear operators in Banach and Hilbert spaces relevant to spectral problems involving differential equations. For the first time it brings together recent results in essential spectra, measures of non-compactness, entropy numbers, approximation numbers, eigenvalues, and the relationships among these concepts. The authors illustrate abstract theory with results for embedding maps between Sobolev spaces. Strong emphasis is placed on application to boundary-value problems for general second-order linear elliptic equations in an arbitrary domain in Rn. The book introduces some key eastern European work, never before available in English translation.