CALCO, the Conference on Algebra and Coalgebra in Computer Science, is a high-level, bi-annual conference formed by joining CMCS (the International WorkshoponCoalgebraicMethodsinComputerScience)andWADT(theWo- shoponAlgebraicDevelopmentTechniques).CALCObringstogetherresearchers and practitioners to exchange new results related to foundational aspects and both traditional and emerging uses of algebras and coalgebras in computer s- ence. The study of algebra and coalgebra relates to the data, process and str- tural aspects of software systems. CALCO is supervised by the Steering C- mittee, co-chaired by Jos' e Luiz Fiadeiro and Jan Rutten. The ?rst two CALCO conferences took place in 2005 in Swansea, Wales, and in 2007 in Bergen, Norway. CALCO 2009, the third event in the series, took place in Udine, Italy, during September 7-10, 2009. CALCO 2009 received 42 submissions, out of which 23 were selected for presentationattheconference.Inspiteofarelativelylownumberofsubmissions, their standard was generally very high. The selection process was carried out by the Program Committee, taking into account the originality, quality and relevance of the material presented in each submission, based on the opinions of expert reviewers, four for each submission. The selected and revised papers are included in this volume, together with the contributions from the invited speakersMaiGehrke,ConorMcBride,PrakashPanangadenandGordonPlotkin.