Summary: We first define polarized proof-nets, an extension of MELL proof-nets for the polarized fragment of linear logic; the main difference with usual proof-nets is that we allow structural rules on any negative formula. The essential properties (confluence, strong normalization in the typed case) of polarized proof-nets are proved using a reduction preserving translation into usual proof-nets. We then give a reduction preserving encoding of Parigot’s \(\lambda \mu\)-terms for classical logic as polarized proof-nets. It is based on the intuitionistic translation: \(A\rightarrow B\), so that it is a straightforward extension of the usual translation of \(\lambda\)-calculus into proof-nets. We give a reverse encoding which sequentializes any polarized proof-net as a \(\lambda \mu\)-term. In the last part of the paper, we extend the \(\sigma\)-equivalence for \(\lambda\)-calculus to \(\lambda \mu\)-calculus. Interestingly, this new \(\sigma\)-equivalence relation identifies normal \(\lambda \mu\)-terms. We eventually show that two terms are equivalent iff they are translated as the same polarized proof-net; thus the set of polarized proof-nets represents the quotient of \(\lambda \mu\)-calculus by \(\sigma\)-equivalence.