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Diagnosing vocal tract pathologies is a task that demands considerable investigation due to the diversity of possible problems and the lack of standards among speech pathologists. Current invasive clinical tools, such as indirect laryngoscopy, videolaryngoscopy, and stroboscopic light, provide quantitative analyses. On the other hand, all diagnoses based on a professional's hearing require subjective identification of problems in the larynx and vocal folds, resulting in a qualitative assessment of the structures. In recent years, there has been a significant motivation to develop software techniques for the noninvasive diagnosis of abnormal functioning of the vocal apparatus by studying the patients' voice signals. Many researchers have proposed larynx models that provide insight into the dynamic behavior of human phonation. This lecture note presents some mathematical model of the larynx that could possibly predict and classify pathologies in the vocal apparatus.