I thought that the closed question here could be modified to a very interesting question (at least as far as big-list type questions go).
Can people name examples of fields of mathematics that were once very active, then fell dormant for a while (and maybe even were forgotten by most people!), and then were revived and became active again?
Here's an example to show what I mean. In the late 19th and early 20th century, hyperbolic geometry was an active and thriving field, attracting the attention of many of the best mathematicians of the era (for instance, Fricke, Klein, Dehn, etc). Fashions changed, however, and the subject was largely forgotten outside of textbooks. In the late '70's, however, Thurston introduced new ideas and showed that hyperbolic geometry was enormously important for the study of 3-manifolds, and now it and its offshoots have become central topics in low-dimensional topology and geometry.
Best Answer
The older theory of Hopf algebras, which grew out of algebraic topology as well as some purely algebraic theories, developed to the level of Sweedler's 1969 book and then became something of a backwater (at least as seen from the outside). But a generation later the study of quantum groups by Drinfeld, Jimbo, and their followers aroused interest in Hopf algebras on a far wider scale than the earlier algebraic work. The "dormancy" period here was not all that long, but I think it's fair to say that the earlier theory stayed mostly outside the mainstream (as measured by ICM programs, top journals, big grants, etc.).