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This paper reports on high-performance Optical Character Recognition (OCR) experiments using Long Short-Term Memory (LSTM) Networks for Greek polytonic script. Even though there are many Greek polytonic manuscripts, the digitization of such documents has not been widely applied, and very limited work has been done on the recognition of such scripts. We have collected a large number of diverse document pages of Greek polytonic scripts in a novel database, called Polyton-DB, containing 15; 689 textlines of synthetic and authentic printed scripts and performed baseline experiments using LSTM Networks. Evaluation results show that the character error rate obtained with LSTM varies from 5.51% to 14.68% (depending on the document) and is better than two well-known OCR engines, namely, Tesseract and ABBYY FineReader.