  Very recently we have witnessed a new development of quantum information, the
so-called continuous variable (CV) quantum information theory. Such a further
development has been mainly due to the experimental and theoretical advantages
offered by CV systems, i.e., quantum systems described by a set of observables,
like position and momentum, which have a continuous spectrum of eigenvalues.
According to this novel trend, quantum information protocols like quantum
teleportation have been suitably extended to the CV framework. Here, we briefly
review some mathematical tools relative to CV systems and we consequently
develop the concepts of quantum entanglement and teleportation in the CV
framework, by analogy with the qubit-based approach. Some connections between
teleportation fidelity and entanglement properties of the underlying quantum
channel are inspected. Next, we face the study of CV quantum teleportation
networks where more users share a multipartite state and an arbitrary pair of
them performs quantum teleportation. In this context, we show alternative
protocols and we investigate the optimal strategy that maximizes the
performance of the network.
