An ideal plasma of electrons and a single species of ions in the low collisionality limit subject to an almost straight magnetic field is considered. In such conditions, the linear theory of transport determines the 3 × 1 matrix of dissipative fluxes [J with circumflex above]r namely, the electric current, the electronic heat flux and the ionic heat flux, in terms of a 3 × 1 matrix of thermodynamic forces [X with circumflex above] combining the electric field with the gradients of the densities and of the temperatures. The classical transport coefficients are the components of the 3 × 3 matrix of tensors [L with circumflex above]rs of the linear flux-force relations [J with circumflex above]r = [summation from s=1 to 9][L with circumflex above]rs[X with circumflex above]. The theory is developed in the framework of the statistical mechanics of charged particles starting from the Landau kinetic equation.