Chapter One gives an exposition of the theory of automorphisms of crossed modules over groupoids. We introduce notions of free derivation and their Whitehead multiplication, and invertible free derivations also called coa.dmissible homotopies. We prove that with this multiplication the set F Der*(C) of all coa.dmissible homotopies is a group and that there is a morphism I::,. : F Der*(C) .- Aut(C) which is a pa.rt of a pre-crossed module which gives rise to a 2-crossed module M(C)->FDer*(C)->Aut(C)

Chapter Two gives a detailed proof of the Brown-Spencer t heorem on the equivalence between crossed modules over groupoids and double groupoids with connection. We define linear coa.dmissible sections for the special double groupoid corresponding to a crossed module, and we prove that the group of all linear coa.dmissible sections and the group of coadmissible homotopies are isomorphic.
Chapter Three genera.lises the notion of "locally Lie groupoicl" to dimension 2 for the special double groupoid called "V-locally Lie double groupoid" and relates this to corresponding notions for crossed modules. We localise the definitions of linear coadmissible sections and coa.drnissible homotopies and prove that these form isomorphic inverse semigroups.
We define a corresponding notion of germ, and from this obtain a holonomy
groupoid as an abstract groupoid H ol('D(C), lVG).
Chapter Four gives the Lie structure on H ol('D(C), WG) and gives its universal property, which shows how a V-loca.lly Lie double groupoid give rise to its holonomy groupoid. This is the main Globalisation Theorem.
Chapter Five gives suggestions for further work in the area.