In Electrical Impedance Tomography (EIT) one wants to image the conductivity distribution of a body from current and voltage measurements carried out on its boundary. In this paper we consider the underlying mathematical model, the inverse conductivity problem, in two dimensions and under the realistic assumption that only a part of the boundary is accessible to measurements. In this framework our data are modeled as a partial Neumann-to-Dirichlet map (ND map). We compare this data to the full-boundary ND map and prove that the error depends linearly on the size of the missing part of the boundary. The same linear dependence is further proved for the difference of the reconstructed conductivities -from partial and full boundary data. The reconstruction is based on a truncated and linearized D-bar method. Auxiliary results include an extrapolation method to estimate the full-boundary data from the measured one, an approximation of the complex geometrical optics solutions computed directly from the ND map as well as an approximate scattering transform for reconstructing the conductivity. Numerical verification of the convergence results and reconstructions are presented for simulated test cases.Neumann-to-Dirichlet data. This is not true any more for partial-boundary data, where the graphs of the two operators represent different subsets of the Cauchy data. This can be further emphasized by the fact that the partialboundary Dirichlet problem is nonphysical in many applications. That is, given a noninsulating body (e.g. a human), applied voltages on a part of the boundary will immediately distribute to the full boundary. Thus, partially supported Dirichlet data do not represent a common physical problem. On the other hand, if one injects current only on a subset Γ ⊂ ∂Ω, the current will stay zero on ∂Ω \Γ. We stress that even in this setting the resulting voltage distribution will be supported on the full-boundary. This is an essential problem for the measurements: we need in our representation the measurement information on ∂Ω. This limitation is overcome by an extrapolation procedure of the measured data, as we will discuss in Section 2.2.Theoretical results for the inverse conductivity problem with partial boundary data mainly concentrate on the uniqueness question. That means, does it follow from infinite-precision data that the conductivities are equal? Uniqueness has been proved in several cases for the Dirichlet-to-Neumann problem, including the important works [4,12,25,28,30]. A thorough survey of these results can be found in [29]. For the more physical Neumann-to-Dirichlet problem there are just a few uniqueness results published. In particular for C 2 conductivities and coinciding measurement and input domains in R 2 by [26], in higher dimensions in [19], and for different input and measurement domains in [9]. A more pratical case with bisweep data has been addressed in [22]. We would like to note that these results are of great importance for the theoretical understanding, but are so far not readily appl...