At the beginning of the 215t century strong efforts are made for facilitating e-learning (electronic-based learning and teaching). This development is driven mainly by economical and technological dynamics, however also the contributions of educational and learning sciences are requested by the decision maker. Beside methodological contributions, cognitive psychology is fundamental for individualising e-learning processes. Essential for individualisation is the adaptivity of the e-learning system - comparable to the teaching behaviour of a private teacher, taking his or her knowledge about the student and the results of learning science into account. The theoretical models and empirical results of cognitive psychology enable us (a) to optimise the individual's learning of specific knowl-edge and skills by adapting the e-learning system to the student's pre-knowledge, to his or her growing knowledge and learning goal, and to the requested kind of comprehension and performance, (b) to optimise individual learning processes by adapting to or improving general learning skills, control processes and learning strategies, as e.g. the repeating schedule with respect to fast learning and long lasting retention, as the communication and co-operation activities, as the cognitive and learning style, and meta cognitive skills ("learning to learn"), and (c) to reduce other cognitive demands during the learning process by the systems adaptivity with respect to the student's cultural background, his or her human-computer-interface preferences as well as to changing learning environments. Realising these forms of adaptivity in e-learning systems by suitable objects of adaptivity on the appropriate level of individualisation of adaptivity needs interdisciplinary co-operation.