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ABSTRACT: Topological Data Analysis (TDA) generally refers to utilizing topological features from data. A typical example is persistent homology. The cluster tree gathers similar data together to make clusters. The persistent homology quantifies salient topological features that appear at different resolutions of the data. TDA provides useful information, such as delivering scientific information from data, or extracting useful features for learning. This talk will be about the application of TDA to machine learning. I will first give brief introduction to Topological Data Analysis: in particular, I will introduce persistent homology and its metric structure. Then I will explain how TDA can be applied to machine learning in two ways: featurization and evaluation. I will present how the persistent homology is featurized in Euclidean space or functional space. Then, I will end this talk by presenting how TDA can be applied to evaluate data or machine learning models.