  This paper describes grope and Whitney tower filtrations on the set of
concordance classes of classical links in terms of class and order
respectively. Using the tree-valued intersection theory of Whitney towers, the
associated graded quotients are shown to be finitely generated abelian groups
under a (surprisingly) well-defined connected sum operation. Twisted Whitney
towers are also introduced, along with a corresponding quadratic enhancement of
the intersection theory for framed Whitney towers that measures Whitney-disk
framing obstructions. The obstruction theory in the framed setting is
strengthened, and the relationships between the twisted and framed filtrations
are described in terms of exact sequences which show how higher-order
Sato-Levine and higher-order Arf invariants are obstructions to framing a
twisted Whitney tower. The results from this paper combine with those in
\cite{CST2,CST3,CST4} to give a classifications of the filtrations; see our
survey \cite{CST0} as well as the end of the introduction. UPDATE: This paper
has been completely subsumed into the paper "Whitney tower concordance of
classical links" \cite{WTCCL}.
