Preface.- Why Would a Mathematician Care About Embryology? M.Gromov.- PART I.BIOLOGICAL BACKGROUND.- Preface to the Biological Part.- Pattern Formation in Regenerating Tissues. A.Hoffmann and P.A. Tsonis.- Gradients and Regulatory Networks of Wnt Signalling in Hydra Pattern Formation. T.W. Holstein.- Modeling of Planar Cell Polarity Signaling. J.D. Axelrod.- Integrated Molecular Circuits for Stem Cell Activity in Arabidopsis Roots. B. Scheres.- The Mechanics of Tissue Morphogenesis. T. Lecuit.- Small Regulatory RNAs and Skeletal Muscle Cell Differentiation. A. Harel-Bellan, A.Polesskaya, I.Naguibneva, M.Ameyar-Zazoua, C.Degerny, J.Kropp, N.Nonne, M.Souidi, G.Kratassiouk, G.Pinna, L.L.Pritchard.- Pattern Formation in Sea Urchin Endomesoderm as Instructed by Gene Regulatory Network Topologies. I.S. Peter and E.H. Davidson.- PART II. MATHEMATICAL MODELS.- Modelling Oscillator Synchronisation During Vertebrate Axis Segmentation. P.J. Murray, P.K. Maini, and R.E. Baker.- Pattern Formation in Hybrid Models of Cell Populations. N. Bessonov, P. Kurbatova, V. Volpert.-An Integrative Approach to the Analysis of Pattern Formation in Butterfly Wings - Experiments and Models. T. Sekimura.- Modeling Morphogenesis in Multicellular Structures with Cell Complexes and L-systems. P. Prusinkiewicz and B. Lane.- Multistability and Hysteresis-based Mechanism of Pattern Formation in Biology. A. Marciniak-Czochra and A. Köthe.- How to knock out feedback Circuits in Gene Networks? H. Gruber, A. Richard, C. Soulé.- Formation of Evolutionary Patterns in Cancer Dynamics. M. Delitala and T. Lorenzi.- How Cell Decides Between Life and Death: Mathematical Modeling of Epigenetic Landscapes of Cellular Fates. A. Zinovyev, L. Calzone, S. Fourquet and E. Barillot.- PART III. IDEAS, HYPOTHESIS, SUGGESTIONS.- From Hydra to Vertebrates: Models for the Transition from Radial- to Bilateral-symmetric Body Plans, H. Meinhardt.- Cell Division and Hyperbolic Geometry. M. Gromov.- Formalistic Representation of the Cellular Architecture in the Course of Plant Tissue Development. I.V. Rudskiy.- The Geometry of Morphogenesis and the Morphogenetic Field Concept. N.Morozova and M.Shubin.- Randomness and Geometric Structures in Biology. V. Capasso.