Abstract The EVA (espacios virtuales de aprendizaje, or virtual learning spaces) project applies artificial intelligence tools to teleteaching methods, in a way that eliminates or mitigates the need for synchronous and in situ education. (A) A taxonomy of the space of knowledge (also called `Learning Space’; currently our prototype teaches M.Sc. courses in Computer Science) is formed and discretized. (B) EVA finds each student’s initial knowledge state (through a computer examination) and final (desired) knowledge state, and from these, a particular learning trajectory is designed for that student. (C) Personalized books (called polybooks, because they are formed by modules (chapters) written in a variety of media) are armed by concatenating — along the learning trajectory — modules from a large pool, and sent to the student through the net in a store-and-forward fashion. (D) EVA searches the net for teaching material which has not been indexed in the discretized learning space, using a tool (Clasitex) inside an agent that finds the main themes or topics that an article (written in natural language) covers. (E) EVA also schedules for each student synchronous activities (lectures in TV, teleconferences, on-line question and answering sessions, chats). (F) EVA suggests for each student suitable `classmates’ (students having similar learning trajectories) in her town, as well as possible advisers (students or alumni having knowledge that the student is acquiring). The present status, problems, models and tools of EVA are presented.