Sweden has a growing number of immigrants, the need for courses and coursebooks in Swedish as a second language (L2) is increasing, as is the demand for standardized tests and qualifications. This project intends to study the development of lexical and grammatical competences in L2 learners of Swedish. We intend to perform the study through two corpora: coursebook texts and learner essays, both marked up for proficiency levels according to the Common European Framework of References (CEFR). The corpora will be processed by computational methods, after which the results will be analysed by linguists, lexicographers, grammarians, teachers and language assessors - both linguistically, and based on theory of teaching, to find ways of identifying minimal or central (need-to-know) vocabulary and grammar scopes, as well as peripheral (good-to-know) grammar and vocabulary at each level of proficiency as a way to support teachers, test-makers, assessor and learners. The aim of this project is, thus, to provide an extensive description of what lexical and grammatical competence learners at each level possess, both receptively and productively, and explore the relation between the receptive and productive scopes. The project will result in a number of practical digital tools: online sites for browsing and downloading lexical and grammatical inventories, and a set of algorithms and tools that can be re-used on other corpora for extraction of similar type of resources.