  The superposition principle lies at the heart of many non-classical
properties of quantum mechanics. Motivated by this, we introduce a rigorous
resource theory framework for the quantification of superposition of a finite
number of linear independent states. This theory is a generalization of
resource theories of coherence. We determine the general structure of
operations which do not create superposition, find an elementary connection to
unambiguous state discrimination, and propose several general quantitative
superposition measures. We show that several main results from resource
theories of coherence still hold in our more general setting. Of special
importance are two results about the free completion of trace decreasing
operations and the free probabilistic transformation between pure states that
are also valid for the special case of coherence.
