Electronic Journal of Differential Equations, Vol. 2013 (2013), No. 101, pp. 1-16. Title: Formally self-adjoint quasi-differential operators and boundary-value problems Authors: Andrii Goriunov (National Academy of Sciences, Kyiv, Ukraine) Vladimir Mikhailets (National Academy of Sciences, Kyiv, Ukraine) Konstantin Pankrashkin (Univ. Paris-Sud 11, Orsay, France) Abstract: We develop the machinery of boundary triplets for one-dimensional operators generated by formally self-adjoint quasi-differential expression of arbitrary order on a finite interval. The technique is then used to describe all maximal dissipative, accumulative and self-adjoint extensions of the associated minimal operator and its generalized resolvents in terms of the boundary conditions. Some specific classes are considered in greater detail. Submitted March 6, 2013. Published April 19, 2013. Math Subject Classifications: 34B05, 34L40, 47N20, 34B37. Key Words: Quasi-differential operator; distributional coefficients; self-adjoint extension; maximal dissipative extension; generalized resolvent.