On stability of minimal surfaces and recent works

This article is an English version of an expository article which appeared originally in Japanese. The purpose of the article is to introduce the fundamental theory of minimal surfaces for non-specialist readers in Japanese. Since it is impossible to achieve all works in this field, we have selected a number of results which seem to be a good guide for beginners. Our aim is to present an outline, and thus there are some parts which we only quote references instead of demonstrating long computations and proofs. After classical arguments, we shall refer to recent works related to triply periodic minimal surfaces which are mathematical models of surfactants.