Language learning and fostering linguistic diversity within the European Union are priorities of the European Commission. Learning new languages can change the structure and function of the cerebral cortex, affecting the way we think. However, despite extensive research, we lack a fine-grained description of how dynamical changes in cortical representations mediate learning concepts and linguistic structures of a new language. The LINGSHIFT program is using a cutting-edge paradigm to identify the dynamic shifts in linguistic representations by addressing three main questions: What are the core cortical regions involved in processing semantics (the meaning of words and sentences) and low-level linguistic information during language learning? What specific semantic or low-level linguistic information do these regions represent? Does the spatial organization of semantic and low-level representations dynamically change over the course of learning a new language? To investigate this, LINGSHIFT combines longitudinal non-invasive brain imaging using naturalistic stimuli and a powerful predictive modelling approach in a multidisciplinary work program. First, LINGSHIFT creates an open-access longitudinal functional MRI language comprehension and production dataset. This dataset will be recorded across a one-year period of adults learning a new language. Second, it identifies the cortical linguistic representations using a predictive modelling approach that makes use of state-of-the-art deep neural network language models. Third, it identifies the dynamical changes in linguistic representations during language acquisition. LINGSHIFT will provide new predictions about long-term dynamics and cortical changes that will improve our understanding of language systems in the brain. It will place important constraints on theoretical frameworks of second language learning that will help modernise language teaching.