Geometric Aspects of Functional Analysis : Israel Seminar 2006–2010 The α Cosine Transform and Intertwining Integrals on Real Grassmannians On Modules Over Valuations On Multiplicative Maps of Continuous and Smooth Functions Order Isomorphisms on Convex Functions in Windows Finite Transitive Graph Embeddings into a Hyperbolic Metric Space Must Stretch or Squeeze Tightness of Fluctuations of First Passage Percolation on Some Large Graphs Finitely Supported Measures on SL2(R) which are Absolutely Continuous at Infinity Interpolations Convexity and Geometric Inequalities Hypercontractive Measures Talagrands Inequality and Inuences A Family of Unitary Operators Satisfying a Poisson Type Summation Formula Stability of Order Preserving Transforms On the Distribution of the 2 Norm of Linear Functionals on Isotropic Convex Bodies A Remark on Vertex Index of the Convex Bodies Inner Regularization of Log Concave Measures and Small Ball Estimates An Operator Equation Generalizing the Leibniz Rule for the Second Derivative Moments of Unconditional Logarithmically Concave Vectors Projections of Probability Distributions: A Measure Theoretic Dvoretzky Theorem On a Loomis Whitney Type Inequality for Permutationally Invariant Unconditional Convex Bodies The Hörmander Proof of the Bourgain Milman Theorem On Some Extension of Feiges Inequality On the Mean Width of Log Concave Approximate Gaussian Isoperimetry for k Sets Remark on Stability of Brunn Minkowski and Isoperimetric Inequalities for Convex Bodies On Contact Points of Convex Bodies This collection of original papers related to the Israeli GAFA seminar (on Geometric Aspects of Functional Analysis) from the years 2006 to 2011 continues the long tradition of the previous volumes which reflect the general trends of Asymptotic Geometric Analysis understood in a broad sense and are a source of inspiration for new research. Most of the papers deal with various aspects of the theory including classical topics in the geometry of convex bodies inequalities involving volumes of such bodies or more generally logarithmically concave measures valuation theory probabilistic and isoperimetric problems in the combinatorial setting volume distribution on high dimensional spaces and characterization of classical constructions in Geometry and Analysis (like the Legendre and Fourier transforms derivation and others). All the papers here are original research papers