The objective of CriticalEarth is to train a cohort of exceptional young scientists, and to advance our understanding of tipping points and assess possible connections between tipping elements in the climate. Fundamental development of the mathematics involved in such multi-scale problems and methods for exploring rare events and critical transitions in computationally heavy state-of-the-art climate models are in focus. The dynamical behavior of complex systems such as the climate in terms of bifurcations and the dependence on stochastic fluctuations as well as the feedbacks involved in the physical processes causing critical transitions will be subject of the research. This is important for underpinning the planetary boundaries and the response to increased levels of greenhouse gases. Ultimately, defining the thresholds for irreversible climate change is a grand scientific challenge and a matter of huge societal importance. Predicting the future climate beyond the linear response to greenhouse forcing, developing early warning systems and quantifying safe operating spaces are challenges for the next generation of scientists. CriticalEarth will train 15 early stage researchers to develop new methods for assessing the mechanisms and associated risks of critical transitions in the climate. The program will enable them to generate, integrate and apply multidisciplinary knowledge from applied mathematics, climate science (paleo and projected future) and numerical simulations. The network will give them an excellent background for collaborating in cross-disciplinary teams in academia, industry, governmental- and non-governmental institutions. CriticalEarth's main outcomes will be (i) a cohort of trained scientists within a research field with high demand for years to come; (ii) a ground-breaking understanding of multiscale dynamics in the Earth system and (iii) better foundations for understanding and better tools for assessing and avoiding irreversible climate change.