Nonstable and stable monomorphisms of vector bundles

In this paper we discuss the existence and classification problem both for nonstable and for stable monomorphisms between given vector bundles. The singularity method supplies invariants (complete in a metastable dimension range), together with methods how to compute them. Particular attention is also paid to stabilization, e.g., to the question how many different nonstable homotopy classes of monomorphisms lie in a stable one.