  We lay the foundations for a theory of divergence-measure fields in
noncommutative stratified nilpotent Lie groups. Such vector fields form a new
family of function spaces, which generalize in a sense the $BV$ fields. They
provide the most general setting to establish Gauss-Green formulas for vector
fields of low regularity on sets of finite perimeter. We show several
properties of divergence-measure fields in stratified groups, ultimately
achieving the related Gauss-Green theorem.
