"Jesuits" are members of a Catholic religious order of men that is more formally called "The Society of Jesus" or, in Latin countries, "The Company of Jesus." The term "Jesuit" was originally meant to be a mocking nickname, but in time it has come into common use. For an introduction to terms and expressions associated with Jesuits and Jesuit education, see "Do you Speak Ignatian?"
Jesuit History
Founded in 1540 by Ignatius Loyola, who was declared a Saint by the Catholic Church in 1622, the Jesuits are the largest Catholic religious order in the world, with more than 18,000 members working in 112 countries. Online resources can offer a quick impression of Jesuits, their history and the state of the Society of Jesus today. For a more leisurely read you might want to consult the chapter, "Ignatius, the Jesuits, and Jesuit Education," in What Are We? An Introduction to Boston College and Its Jesuit Tradition.
For a standard history of the Jesuits in English, see William V. Bangert's A History of the Society of Jesus (Institute of Jesuit Sources, June 1986). The most authoritative discussion of the early Jesuits is by John O'Malley, The First Jesuits (Harvard University Press, 1993)
There is not enough material on an important part of Jesuit history, namely, its suppression in the late 18th century. Recently, Loyola Press has done a great service in presenting On the Suppression of the Society of Jesus, A Contemporary Account, by Giulio Cesare Cordara, S.J., translation and notes by John P. Murphy, S.J. Perhaps the highest recommendation we can give this volume is that of John O'Malley who says that this volume is a "page turner -- it reads almost as if it were written yesterday."