This paper presents the organizational framework adopted by the Academic League of Artificial Intelligence (LIA) at the Federal University of Santa Catarina (UFSC), designed to integrate teaching, research, and university extension through a student-centered, project-based approach. The framework combines democratic governance, collaborative learning, and dynamic project organization to foster both technical and transversal competencies. Representative initiatives, including competition teams, study groups, open lectures, knowledge repositories, and AI-powered applications with social impact, demonstrate how diverse educational, scientific, and extension activities can be developed within a common organizational structure while promoting leadership, scientific production, community engagement, and knowledge preservation. Blogger's Review: The proposed framework provides a flexible and replicable model for integrating the three university pillars into engineering and computing education, offering practical guidance for academic leagues and similar student organizations.