IBM models for word alignment. Many-to-one and many-to-many alignments. IBM model 1 and the HMM alignment model. Training the alignment models: the Expectation Maximization (EM) algorithm. Symmetrizing alignments for phrase-based MT: symmetrizing by intersection; the growing heuristic. Calculating the phrase translation table. Decoding: stack decoding. Evaluation of MT systems. BLEU. Log-linear models for MT.