This monograph describes mathematical methods applicable to studying nonclassical problems of mathematical physics. The emphasis of the book is on applications of the interpolar theory of Banach spaces to the theory of linear operators to be expotentially dichotomous, to some continuity properties of linear operators in Hilbert scales, to the Riesz basis property of eigenelements and associated elements of linear pencils and the correspondending elliptic problems with indefinite weight functions, and to studying nonclassical boundary value problems for first order operator-differential equations.