Higgs physics at a high luminosity e+e- linear collider

Since the TESLA Technical Design Report (TDR) was published in 2001, the physics programme of an electron-positron linear collider (LC) has been further developed and a wide consensus has been reached on the physics case and the need for a high luminosity LC with center-of-mass energy up to about 1 TeV as the next worldwide high-energy physics project. The study of the Higgs boson properties represents a significant part of this physics programme. New studies demonstrate that a LC providing 1000 fb(-1) of data at center-of-mass energies of at least 500 GeV, is an excellent Higgs boson analyzer for a wide range of masses. A summary of preliminary results of these studies and their implications for identifying the nature of the Higgs sector and for constraining the parameter space of extended models is given. The focus is on recent developments and the relation to the LHC is addressed.