  Firstly, we wish to motivate that Conley pairs, realized via Salamon's
definition [17], are rather useful building blocks in geometry: Initially we
met Conley pairs in an attempt to construct Morse filtrations of free loop
spaces [21]. From this fell off quite naturally, firstly, an alternative proof
[20] of the cell attachment theorem in Morse theory [13] and, secondly, some
ideas [12] how to try to organize the closures of the unstable manifolds of a
Morse-Smale gradient flow as a CW decomposition of the underlying manifold.
Relaxing non-degeneracy of critical points to isolatedness we use these Conley
pairs to implement the gradient flow proof of the Lusternik-Schnirelmann
Theorem [10] proposed in Bott's survey [3].
  Secondly, we shall use this opportunity to provide an exposition of
Lusternik-Schnirelmann (LS) theory based on thickenings of unstable manifolds
via Conley pairs. We shall cover the Lusternik-Schnirelmann Theorem [10],
cuplength, subordination, the LS refined minimax principle, and a variant of
the LS category called ambient category.
