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A detailed description will be provided of all the classification algorithms that have been widely used in the domain of medical science. The foundation will be laid by giving a comprehensive overview pertaining to the background and history of the classification algorithms. This will be followed by an extensive discussion regarding various techniques of classification algorithm in machine learning (ML) hence concluding with their relevant applications in data analysis in medical science and health care. To begin with, the initials of this chapter will deal with the basic fundamentals required for a profound understanding of the classification techniques in ML which will comprise of the underlying differences between Unsupervised and Supervised Learning followed by the basic terminologies of classification and its history. Further, it will include the types of classification algorithms ranging from linear classifiers like Logistic Regression, Naïve Bayes to Nearest Neighbour, Support Vector Machine, Tree-based Classifiers, and Neural Networks, and their respective mathematics. Ensemble algorithms such as Majority Voting, Boosting, Bagging, Stacking will also be discussed at great length along with their relevant applications. Furthermore, this chapter will also incorporate comprehensive elucidation regarding the areas of application of such classification algorithms in the field of biomedicine and health care and their contribution to decision-making systems and predictive analysis. To conclude, this chapter will devote highly in the field of research and development as it will provide a thorough insight to the classification algorithms and their relevant applications used in the cases of the healthcare development sector.