This chapter gives an introduction to lattice QCD at finite temperature and baryon density. After a discussion of some fundamental aspects and difficulties of quantum field theory at finite temperature in the continuum, the lattice formulation of the partition function for the grand canonical ensbemble is introduced and its relation to the transfer matrix formalism is presented. As analytic tools for its evaluation, weak coupling perturbation theory on the lattice as well as the strong coupling expansion are discussed. Regarding Monte Carlo evaluations, similarities and differences to the situation in the vacuum are pointed out. All concepts are illustrated with various applications like the equation of state, screening masses, the free energy of static quark systems and phase transitions. In the second part, special emphasis is put on lattice QCD at finite baryon density. The sign problem is discussed and current techniques to deal with it at small baryon chemical potential are presented. The implications for the QCD phase diagram are summarized.

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