Planarity is a research area in mathematics and computer science that focuses on studying graphs and their embeddings in two-dimensional space without edge crossings. A graph is considered planar if it can be drawn in such a way that no two edges intersect each other. This area of research involves exploring the properties, algorithms, and applications of planar graphs, as well as studying how to efficiently test whether a given graph is planar. Planarity is a fundamental concept in graph theory and has important applications in various fields, including network design, circuit layout, and computational geometry.