The main objective is to present an off-line signature verification system. It is basically divided into three parts. The first demonstrates a pre-processing process, a segmentation process and a feature extraction process, in which the main aim is to obtain the maximum performance quality of the process of verification of random falsifications, in the false acceptance and false rejection concept. The second presents a learning process based on HMM, where the aim is obtaining the best model. That is, one that is capable of representing each writer's signature, absorbing yet at the same time discriminating, at most the intrapersonal and interpersonal variation. The third presents a signature verification process that uses the models generated by the learning process without using any prior knowledge of test data, in other words, using an automatic derivation process of the decision thresholds.