Abstract: A measurement of the associated production of a top-quark pair (t (t) over bar) with a vector boson (W, Z) in proton-proton collisions at a center-of-mass energy of 13 TeV is presented, using 36.1 fb(-1) of integrated luminosity collected by the ATLAS detector at the Large Hadron Collider. Events are selected in channels with two same- or opposite-sign leptons (electrons or muons), three leptons or four leptons, and each channel is further divided into multiple regions to maximize the sensitivity of the measurement. The t (t) over barZ and t (t) over barW production cross sections are simultaneously measured using a combined fit to all regions. The best-fit values of the production cross sections are sigma(t (t) over barZ) = 0.95 +/- 0.08(stat )+/- 0.10(syst) pb and sigma(t (t) over barW) = 0.87 +/- 0.13(stat) +/- 0.14(syst) pb in agreement with the Standard Model predictions. The measurement of the t (t) over barZ cross section is used to set constraints on effective field theory operators which modify the t (t) over barZ vertex.