  We present high-resolution Magellan/MIKE spectroscopy of 42 red giant stars
in seven stellar streams confirmed by the Southern Stellar Stream Spectroscopic
Survey (S5): ATLAS, Aliqa Uma, Chenab, Elqui, Indus, Jhelum, and Phoenix.
Abundances of 30 elements have been derived from over 10,000 individual line
measurements or upper limits using photometric stellar parameters and a
standard LTE analysis. This is currently the most extensive set of element
abundances for stars in stellar streams. Three streams (ATLAS, Aliqa Uma, and
Phoenix) are disrupted metal-poor globular clusters, although only weak
evidence is seen for the light element anticorrelations commonly observed in
globular clusters. Four streams (Chenab, Elqui, Indus, and Jhelum) are
disrupted dwarf galaxies, and their stars display abundance signatures that
suggest progenitors with stellar masses ranging from $10^6-10^7 M_\odot$.
Extensive description is provided for the analysis methods, including the
derivation of a new method for including the effect of stellar parameter
correlations on each star's abundance and uncertainty.
  This paper includes data gathered with the 6.5 meter Magellan Telescopes
located at Las Campanas Observatory, Chile.
