  We study NSOP$_{1}$ theories. We define Kim-independence, which generalizes
non-forking independence in simple theories and corresponds to non-forking at a
generic scale. We show that Kim-independence satisfies a version of Kim's
lemma, local character, symmetry, and an independence theorem and that,
moreover, these properties individually characterize NSOP$_{1}$ theories. We
describe Kim-independence in several concrete theories and observe that it
corresponds to previously studied notions of independence in Frobenius fields
and vector spaces with a generic bilinear form.
