The understanding of toxicity is of paramount importance to human health and environmental protection. Quantitative toxicity analysis has become a new standard in the field. This work introduces element specific persistent homology (ESPH), an algebraic topology approach, for quantitative toxicity prediction. ESPH retains crucial chemical information during the topological abstraction of geometric complexity and provides a representation of small molecules that cannot be obtained by any other method. To investigate the representability and predictive power of ESPH for small molecules, ancillary descriptors have also been developed based on physical models. Topological and physical descriptors are paired with advanced machine learning algorithms, such as the deep neural network (DNN), random forest (RF), and gradient boosting decision tree (GBDT), to facilitate their applications to quantitative toxicity predictions. A topology based multitask strategy is proposed to take the advantage of the availability of large data sets while dealing with small data sets. Four benchmark toxicity data sets that involve quantitative measurements are used to validate the proposed approaches. Extensive numerical studies indicate that the proposed topological learning methods are able to outperform the state-of-the-art methods in the literature for quantitative toxicity analysis. Our online server for computing element-specific topological descriptors (ESTDs) is available at http://weilab.math.msu.edu/TopTox/ .