The project AlgoKnot aims at strengthening our understanding of the computational and combinatorial complexity of the diverse facets of knot theory, as well as designing efficient algorithms and software to study their interconnections. The study of knots as mathematical objects has triggered the emergence of a plethora of techniques from topology, combinatorics, geometry, and algebra. This variety is reflected by the richness of the computational complexity and algorithms for these diverse properties of knots. Moreover, among the deepest mathematical conjectures in the field predict subtle connections between knot invariants of distinct nature. Extensive experiments play a fundamental role in verify these conjectures. The project consequently aims at refining our understanding of the complexity of computing knot invariants, as well as designing faster algorithms to compute them, and performing extensive experiments to verify mathematical conjectures.