  The cell-attachment problem, perhaps first studied by J.H.C. Whitehead around
1940, asks one to describe the effect of attaching one or more cells, on the
algebraic invariants of a topological space. This thesis studies the effect of
cell attachments on loop space homology. It generalizes previous work by D.
Anick on spherical 2-cones, and S. Halperin, J.-M. Lemaire and others on inert
attaching maps.
  It is assumed that the loop space homology of the base space is torsion-free.
Two classes of attaching maps are introduced: free and semi-inert attaching
maps. For these cases, the loop space homology is calculated as a module and as
an algebra, respectively, and is shown to have a surprisingly simple form.
These results are also presented in terms of extensions of differential graded
algebras.
  The second part of the thesis uses Adams-Hilton models and the previous
results to prove that the loop space homology of certain CW complexes is
generated by Hurewicz images. This can sometimes be used to show that the loop
space of a finite complex is, after localizing away from finitely many primes,
homotopy equivalent to a product of spheres and loops on spheres.
  A lemma, which may of independent interest, generalizes the Schreier
property, which states that a Lie subalgebra of a free (graded) Lie algebra is
also a free Lie algebra.
