Linear ODEs: an Algebraic Perspective

This booklet was intended to provide a minimum of ready-to-use references for the minicourse given by the author during the XXII E ́scola de Algebra (40 Anos), held in Salvador de Bahia (July 2012). It wishes to bring to the fore a number of relationships with other branches of mathematics. Examples include the theory of symmetric functions, the theory of universal decomposition algebras associated to a polynomial, derivations of the exterior algebra of a free module, D-modules, Schubert calculus for the complex Grassmannian, boson–fermion correspondence in the representation theory of the Heisenberg algebra.