This volume is a collection of dedicated reviews covering all aspects of theoretical high energy physics and some aspects of solid state physics. Some of the papers are broad reviews of topics that span the entire field while others are surveys of authors' personal achievements. This is the most comprehensive review collection reflecting state of the art at the end of 2004. An important and unique aspect is a special effort the authors have invested in making the presentation pedagogical.

The book aims to analyze and explore deep and profound relations between string field theory, higher spin gauge theories and holography — the disciplines that have been on the cutting edge of theoretical high energy physics and other fields. These intriguing relations and connections involve some profound ideas in number theory, which appear to be part of a unifying language to describe these connections.

Physicists argue from different perspectives for and against the idea of the existence of multiple universes.

This proceedings is based on the interdisciplinary workshop held in Madrid, 5-9 March 2018, dedicated to Alberto Ibort on his 60th birthday. Alberto has great and significantly contributed to many fields of mathematics and physics, always with highly original and innovative ideas.Most of Albertos’s scientific activity has been motivated by geometric ideas, concepts and tools that are deeply related to the framework of classical dynamics and quantum mechanics.Let us mention some of the fields of expertise of Alberto Ibort:Geometric Mechanics; Constrained Systems; Variational Principles; Multisymplectic structures for field theories; Super manifolds; Inverse problem for Bosonic and Fermionic systems; Quantum Groups, Integrable systems, BRST Symmetries; Implicit differential equations; Yang-Mills Theories; BiHamiltonian Systems; Topology Change and Quantum Boundary Conditions; Classical and Quantum Control; Orthogonal Polynomials; Quantum Field Theory and Noncommutative Spaces; Classical and Quantum Tomography; Quantum Mechanics on phase space; Wigner-Weyl formalism; Lie-Jordan Algebras, Classical and Quantum; Quantum-to-Classical transition; Contraction of Associative Algebras; contact geometry, among many others.In each contribution, one may find not only technical novelties but also completely new way of looking at the considered problems. Even an experienced reader, reading Alberto's contributions on his field of expertise, will find new perspectives on the considered topic.His enthusiasm is happily contagious, for this reason he has had, and still has, very bright students wishing to elaborate their PhD thesis under his guidance.What is more impressive, is the broad list of rather different topics on which he has contributed.

This is the first volume in a series of books on the general theme of Supersymmetric Mechanics; the series is based on lectures and discussions held in 2005 and 2006 at the INFN-Laboratori Nazionali di Frascati. The selected topics include supersymmetry and supergravity, the attractor mechanism, black holes, fluxes, noncommutative mechanics, super-Hamiltonian formalism and matrix models. Incorporates in extensive write-ups the results of animated discussion sessions which followed the individual lectures.

Casimir forces between spheres and loop integrals / J. Babington -- Analytic corrections to the electromagnetic Casimir interaction between a sphere and a plate at short distances / M. Bordag and V. Nikolaev -- Casimir physics : geometry, shape and material / T. Emig -- Semitransparent pistons / P. Morales and K. Kirsten -- Using boundary methods to compute the Casimir energy / F.C. Lombardo, F.D. Mazzitelli and P.I. Villar -- Electromagnetic non-contact gears : prelude / P. Parashar [und weitere] -- The scattering approach to the Casimir force / S. Reynaud [und weitere] -- Scalar Casimir energies for separable coordinate systems : application to semi-transparent planes in an annulus / J. Wagner, K.A. Milton and K. Kirsten -- Demonstrating the strong geometry dependence of the Casimir force on a surface with deep, nanoscale corrugations / H.B. Chan [und weitere] -- New results for the Casimir interaction : sample characterization and low temperature measurements / R.S. Decca, D. Lopez and E. Osquiguil -- Casimir force experiments in air : two birds with one stone / S. De Man [und weitere] -- Experimental features of the recent lateral Casimir force measurement / H.-C. Chiu and U. Mohideen -- Lateral Casimir-Polder force measurement using Bose Einstein condensates / G.A. Moreno -- Repulsive Casimir and van der Waals forces : from measurements to future technologies / J.N. Munday and F. Capasso -- Macroscopic quantum vacuum and microscopic gravitation / R. Onofrio -- The PVLAS experiment and its results : probing the quantum vacuum with polarized light and magnetic fields / F. Della Valle [und weitere] -- Thermal Casimir effect for conducting plates and the Bohr-van Leeuwen theorem / G. Bimonte -- Electromagnetic Casimir effect in wedge geometry and the energy-momentum tensor in media / I. Brevik, S.A. Ellingsen and K.A. Milton -- Casimir-Polder potential in thermal non-equilibrium / S.A. Ellingsen [und weitere] -- Geometry-temperature interplay in the Casimir effect / H. Gies and A. Weber -- Thermal effects in the magnetic Casimir-Polder interaction / H. Haakh, F. Intravaia and C. Henkel -- Mode contributions to the Casimir effect / F. Intravaia and C. Henkel -- Thermal Casimir force between magnetic materials / G.L. Klimchitskaya, B. Geyer and V.M. Mostepanenko -- The Casimir effect and the foundations of statistical physics / V.M. Mostepanenko and G.L. Klimchitskaya -- Casimir-Lifshitz forces and entropy / L.P. Pitaevskii -- The thermal Casimir effect : saturation / B.E. Sernelius -- Finite temperature Casimir effect in the presence of extra dimensions / L.P. Teo and K. Kirsten -- The role of magnetoplasmons in Casimir force calculations / R. Esquivel-Sirvent [und weitere] -- Suspended graphene films and their Casimir interaction with ideal conductor / I.V. Fialkovsky -- Casimir energy of finite width mirrors : renormalization, self-interaction limit and Lifshitz formula / I.V. Fialkovsky, V.N. Markov and Yu. M. Pis'mak -- Role of surface states in the Casimir force between semiconducting films / M. Govoni, C. Calandra and A. Benassi -- On the Casimir entropy between "perfect crystals" / C. Henkel and F. Intravaia -- Theory of the Casimir effect for gratings / V.N. Marachevsky