Differential and more general self-adjoint operators involving singular interactions arise naturally in a range of subjects such as classical and quantum physics, chemistry, and electronics. This book is a systematic mathematical study of these operators, with particular emphasis on spectral and scattering problems. The methods discussed are based on a new concept of symplectic structure of the "boundary form." Suitable for researchers in analysis or mathematical physics, this volume could also be used as a text for an advanced course on the applications of analysis.