Recent advances in computational geometry and computational topology have made it possible to compute topological invariants of sets and functions from sample points. These types of data summaries provide new tools for preprocessing, summarizing and visualizing complex and even high dimensional data. As a result, the number and the variety of applications of topological data-analytic methods have been growing rapidly. Despite such increase in popularity, the statistical properties and effectiveness of the methodologies of topological data analysis, as well as their potential for offering novel tools for statistical inference, remain largely unexplored. This tutorial will provide a broad overview of frequentist statistical inference for researchers with background in algebraic topology and computational geometry. I will first describe the key inferential tasks of parameter estimation, hypothesis testing and uncertainty assessment by confidence sets. I will then cover more advanced topics in statistical inference, such as minimality and nonparametric statistics. Throughout the tutorial I will rely as much as possible on examples that are directly relevant to topological data analysis.