A set of lines in a Euclidean space is called equiangular if any pair of lines forms the same angle. The study of equiangular lines is related to many things such as energy minimizing configurations, line packing problems, and kissing number problems. In this talk we start with Neumann’s theorem which gives necessary conditions on the angles with which the lines intersects with each other if there are many equiangular lines. Then we will give several constructions of large equiangular sets, most of which come from the design theory. Finally we propose to combine integral lattices and graph theory to generate equiangular sets of lines.
 Petrus W. H. Lemmens and Johan J. Seidel, Equiangular lines, Journal of Algebra 24 (1973), no. 3, 494–512.
 Yen-chi Roger Lin and Wei-Hsuan Yu, Equiangular lines and the Lemmens-Seidel conjecture, Discrete Mathematics 343 (2020), no. 2, 111667.
 Yen-chi Roger Lin and Wei-Hsuan Yu, Saturated configuration and new construction of equiangular lines, Linear Algebra and its Applications 588 (2020), 272–281.