This article presents the primitive elements theory of cognitive skills. The central idea is that skills are broken down into primitive information processing elements that move and compare single pieces of information regardless of the specific content of this information. Several of these primitive elements are necessary for even a single step in a task. A learning process therefore combines the elements in increasingly larger, but still context-independent, units. If there is overlap between tasks, this means the larger units learned for 1 task can be reused for the other task, producing transfer. The theory makes it possible to construct detailed process models of 2 classic transfer studies in the literature: a study of transfer in text editors and 1 in arithmetic. I show that the approach produces better fits of the amount of transfer than Singley and Anderson's (1985) identical productions model. The theory also offers explanations for far transfer, in which the 2 tasks have no surface characteristics in common, which I demonstrate with 2 models in the domain of cognitive control, where training on either task-switching or working memory control led to an improvement of performance on other control tasks. The theory can therefore help evaluate the effectiveness of cognitive training that has the goal to improve general cognitive abilities.