Finite groups in integral group rings

Notes used for a course held in 2016 in the School of Advances in Group Theory and Applications, for some lectures given in 2018 for the students of the Master in Mathematics of the Vrije Universiteit Brussels, a course for master and Ph.D. students at the Universidade de S~ao Paulo and at the conference Group algebras, representations and computations. We revise some problems on the study of finite subgroups of the group of units of integral group rings of finite groups and some techniques to attack them.