  We present a detailed analysis of 2-complete stable homotopy groups, both in
the classical context and in the motivic context over C. We use the motivic May
spectral sequence to compute the cohomology of the motivic Steenrod algebra
over C through the 70-stem. We then use the motivic Adams spectral sequence to
obtain motivic stable homotopy groups through the 59-stem. In addition to
finding all Adams differentials in this range, we also resolve all hidden
extensions by 2, eta, and nu, except for a few carefully enumerated exceptions
that remain unknown. The analogous classical stable homotopy groups are easy
consequences.
  We also compute the motivic stable homotopy groups of the cofiber of the
motivic element tau. This computation is essential for resolving hidden
extensions in the Adams spectral sequence. We show that the homotopy groups of
the cofiber of tau are the same as the E2-page of the classical Adams-Novikov
spectral sequence. This allows us to compute the classical Adams-Novikov
spectral sequence, including differentials and hidden extensions, in a larger
range than was previously known.
