This book constitutes the refereed proceedings of the Second International Conference on Algebraic Informatics, CAI 2007, held in Thessaloniki, Greece, in May 2007. The 10 revised full papers presented together with 9 invited papers were carefully reviewed and selected from 29 submissions. The papers cover topics such as algebraic semantics on graphs and trees, formal power series, syntactic objects, algebraic picture processing, infinite computation, acceptors and transducers for strings, trees, graphs, arrays, etc., and decision problems.