  We present a Galois theory of parameterized linear differential equations
where the Galois groups are linear differential algebraic groups, that is,
groups of matrices whose entries are functions of the parameters and satisfy a
set of differential equations with respect to these parameters. We present the
basic constructions and results, give examples, discuss how isomonodromic
families fit into this theory and show how results from the theory of linear
differential algebraic groups may be used to classify systems of second order
linear differential equations.
