  In a series of papers, we will develop systematically the basic spectral
theory of (self-adjoint) boundary value problems for operators of Dirac type.
We begin in this paper with the characterization of (self-adjoint) boundary
conditions with optimal regularity, for which we will derive the heat
asymptotics and index theorems in subsequent publications. Along with a number
of new results, we extend and simplify the proofs of many known theorems.
  Our point of departure is the simple structure which is displayed by Dirac
type operators near the boundary. Thus our proofs are given in an abstract
functional analytic setting, generalizing considerably the framework of compact
manifolds with boundary.
  The results of this paper have been announced in math.DG/9902100

Functional Analysis;Differential Geometry