**Authors:** editor Linfan Mao

The First International Conference on Smarandache Multispace and Multistructure was organized by Prof. Linfan Mao, and it was held in the Beijing University of Civil Engineering and Architecture of P. R. China on June 28-30, 2013. There were 46 researchers from China, India, Iran, Nigeria, and USA that have taken part in this conference with 14 papers on Smarandache multispace and geometry, birings, neutrosophy,neutrosophic groups, regular maps and topological graphs with applications to non-solvable equation systems. Definition. In any domain of knowledge, a Smarandache multispace (or S-multispace) with its multistructure is a finite or infinite (countable or uncountable) union of many spaces that have various structures. The spaces may overlap. The notions of multispace (also spelt multi-space) and multi- structure (also spelt multi-structure) were introduced by Smarandache in 1969 under his idea of hybrid science: combining different fields into a unifying field, which is closer to our real life world since we live in a heterogeneous space. Today, this idea is widely accepted by the world of sciences. S-multispace is a qualitative notion, since it is too large and includes both metric and non-metric spaces. It is believed that the smarandache multispace with its multistructure is the best candidate for 21st century Theory of Everything in any domain. It unifies many knowledge fields. Applications. A such multispace can be used for example in physics for the Unified Field Theory that tries to unite the gravitational, electromagnetic, weak and strong interactions. Or in the parallel quantum computing and in the mu-bit theory, in multi-entangled states or particles and up to multi-entangles objects. We also mention: the algebraic multispaces (multi-groups, multi-rings, multi-vector spaces, multi-operation systems and multi-manifolds, also multi-voltage graphs, multi-embedding of a graph in an n-manifold, etc.), geometric multispaces (combinations of Euclidean and Non-Euclidean geometries into one space as in Smarandache geometries), theoretical physics, including the relativity theory, the M-theory and the cosmology, then multi-space models for p-branes and cosmology, etc. - The multispace and multistructure were first used in the Smarandache geometries (1969), which are combinations of different geometric spaces such that at least one geometric axiom behaves differently in each such space. - In paradoxism (1980), which is a vanguard in literature, arts, and science, based on finding common things to opposite ideas [i.e. combination of contradictory fields]. - In neutrosophy (1995), which is a generalization of dialectics in philosophy, and takes into con- sideration not only an entity < A > and its opposite < antiA > as dialectics does, but also the neutralities < neutA > in between. Neutrosophy combines all these three < A >,< antiA > and < neutA > together. Neutrosophy is a metaphilosophy. - Then in neutrosophic logic (1995), neutrosophic set (1995), and neutrosophic probability (1995), which have, behind the classical values of truth and falsehood, a third component called indeterminacy (or neutrality, which is neither true nor false, or is both true and false simultaneously - again a combination of opposites: true and false in indeterminacy). - Also used in Smarandache algebraic structures (1998), where some algebraic structures are in- cluded in other algebraic structures.

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