TAILOR is a European network developing the scientific foundations for realising the European vision of human-centred Trustworthy AI. To achieve this, we strongly believe that it is necessary to combine and integrate learning, optimisation and reasoning. TAILOR is one of four EU-funded networks of AI research excellence centers. One of our most important tools is the TAILOR Strategic Research and Innovation Roadmap.  It is our ambition that the roadmap will identify major scientific research challenges and push the scientific progress towards the most pressing challenges. It is based on input from both industry and academia, especially working groups related to the five research themes of TAILOR and a series of theme development workshops organised in close collaboration with industry. This document is the first version of the roadmap. It should be considered a living document that acts as a starting point for this important initiative. Even though it is a snapshot of the current situation, it also contains short- and long-term recommendations for the direction of future European AI research.