This course aims at providing fundamental and advanced concepts for the analysis and design of composite materials and structures. In particular, lectures cover the following main topics: structural theories and finite element modelling, failure and damage analysis, optimization and tailoring, multiscale approaches, impact problems, manufacturing, and applications. The lecturers have strong professional backgrounds in material science and structural mechanics. They are currently involved in many international research projects on composites, and industrial partnerships, including Airbus, Boeing, Embraer, and NASA. Most of the Lecturers are currently involved in Marie Curie European Training Network projects on composite materials and structures, FULLCOMP (www.fullcomp.net) and COACH (http://www.coach-etn.eu/). The first module of the course provides basic concepts related to laminated structures, the theory of anisotropic bodies, and the peculiarities of advanced composite materials. Then, the course continues with a review of classical and advanced theories and computational models for laminated structures. Particular attention is paid to beams, plates, and shells, and including guidelines and recommendations for a proper finite element modeling. The second module focuses on the manufacturing processes and the applications of composites. First, this module deals with typical issues such as joining and coating. Then, an overview follows on advanced manufacturing for aerospace applications, glasses, and composites for health care, energy production, and ICT. Recent advances in low-cost composites and composites from waste close this module. The third module offers insights on design and optimization of composite structures. Lectures deal with some of the most important methods related to tailoring, tow placement, microstructural tailoring, suppression and mitigation of buckling, multistability, and morphing. The fourth module deals with the multiscale analysis, failure, and delamination. After an introduction to the modeling of composite material and structures, the modelling damage and failure of laminates follow. Then, the core part is on details on multiscale approaches for the simulation of composite material and structure at the micro meso and macro scales. The fifth module is on impact problems. First, contact laws and impact dynamics concepts open this module. Then, assessments on some of the most important impacts for composites follow; that is, low-velocity impact damage, ballistic impact, explosions. Experimental techniques, numerical models, and guidelines on the design for impact resistance close this module. The sixth module of the course deals with the design of lightweight, composite shells. This module covers some of the most important issues related to composite shells; that is stability, nonlinearity, imperfections, and probabilistic optimization. Furthermore, an introduction to the material behavior at different scales, quasi-static and fatigue failure, and the design and analysis of structural joints follow. The course is addressed to most of the European Ph.D. schools with curricula in structural mechanics, and material science. Also, researchers and professionals dealing with the design and analysis of advanced structures for aeronautics, space, naval, automotive, biomedical applications, and material science could be interested in the course as well as researchers and professionals dealing with the design and analysis of advanced structures for aeronautics, space, naval, automotive, and biomedical applications.