  We prove a rigidity theorem that shows that, under many circumstances,
quasi-isometric embeddings of equal rank, higher rank symmetric spaces are
close to isometric embeddings. We also produce some surprising examples of
quasi-isometric embeddings of higher rank symmetric spaces. In particular, we
produce embeddings of $SL(n,\mathbb R)$ into $Sp(2(n-1),\mathbb R)$ when no
isometric embeddings exist. A key ingredient in our proofs of rigidity results
is a direct generalization of the Mostow-Morse Lemma in higher rank. Typically
this lemma is replaced by the quasi-flat theorem which says that maximal
quasi-flat is within bounded distance of a finite union of flats. We improve
this by showing that the quasi-flat is in fact flat off of a subset of
codimension $2$.
