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Our research project utilizes rigorous techniques from topological data analysis, a type of data analysis based on a mathematical field known as algebraic topology and machine learning, to computationally visualize and analyze electrocardiogram (ECG) data of patients with various heart conditions, including Ventricular Tachycardia, Ventricular Flutter, and Ventricular Fibrillation. By leveraging sophisticated analysis tools such as persistent homology and simplicial complexes, including the Vietoris Rips Complex, we obtain a highly precise modeling of the ECG data, enabling us to distinguish between the ECG data of patients suffering from these debilitating illnesses from healthy individuals. Our novel approach involves extracting critical geometric features from the persistence diagrams and images obtained from our persistent homologies of the patient ECG data. These features are then input into an algorithm based on our topological data analysis, enabling us to classify, with virtually complete accuracy, which of these three conditions a patient is suffering from. Our research project represents a key step forward in the field of heart disease diagnosis, potentially offering a non-invasive, highly accurate method for diagnosing the hundreds of thousands of patients suffering from these conditions.