In statistical machine learning, avoiding density estimation is essential because it is often more difficult than solving a target machine learning problem itself. This is often referred to as Vapnik's principle, and the support vector machine is one of the successful realizations of this principle. Following this spirit, a new machine learning framework based on the ratio of probability density functions has been introduced recently. This density-ratio framework includes various important machine learning tasks such as transfer learning, outlier detection, feature selection, clustering, and conditional density estimation. All these tasks can be effectively and efficiently solved in a unified manner by direct estimating the density ratio without going through density estimation. In this lecture, I give an overview of theory, algorithms, and application of density ratio estimation.