In this volume, five papers are collected that give a good sample of the problems and the results characterizing some recent trends and advances in this theory. Some of them are devoted to the improvement of a general abstract knowledge of the behaviour of elastic bodies, while the others mainly deal with more applicative topics. The first paper entitled "Collected Results on Finite Amplitude Plane Waves in Deformed Mooney-Rivlin Materials" by Ph. Boulanger and M. Hayes gives a complete and systematic exposition of a body of selected results concerning the propagation of finite-amplitude plane waves in a deformed Mooney-Rivlin material. C.O. Horgan's paper entitled "Decay Estimates for Boundary Value Problems in Linear and Nonlinear Continuum Mechanics" provides a review of recent results concerning the decay at large spatial distance of solutions to (systems of) elliptic partial differential equations. In the third paper "On the Traction Problem in Incompressible Linear Elasticity for Unbounded Domains" by R. Russo and G. Starita, the well-posedness (existence, uniqueness and continuous dependence of solutions upon the data) of the traction problem in incompressible linear elasticity for three-dimensional exterior domains is proved in the class of solutions with finite energy. The paper contributed by T. Valent "An Abstract Perturbation Problem with Symmetries Suggested by Live Boundary Problems in Elasticity" deals with an abstract formulation for boundary problems with symmetries, and with a study of a general perturbation problem with symmetries. The fifth paper "Maximum Principles in Classical Elasticity" by L.T. Wheeler, owes its interest to a wide discussion of the applications of maximum principles for scalar-valued functions to classical theory of elasticity 1. On the Degrees Less Than 0', Ann. Math. 77 (1963) 211-231 -- 2. Recursive Enumerability and the Jump Operator, Trans. Amer. Math. Soc. 108 (1963) 223-239 -- 3. Recursively Enumerable Degrees are Dense, Ann. Math. 80 (1964) 300-312 -- 4. Simple Set Which is Not Effectively Simple, Proc. Amer. Math. Soc. 15 (1964) 51-55 -- 5. Metarecursive Sets / G. E. Sacks and Georg Kreisel, J. Symbolic Logic 30 (1965) 318-338 -- 6. Post's Problem, Admissible Ordinals, and Regularity, Trans. Amer. Math. Soc. 124 (1966) 1-23 -- 7. On a Theorem of Lachlan and Martin, Proc. Amer. Math. Soc. 18 (1967) 140-141 -- 8. Minimal Hyperdegree / G. E. Sacks and Robin O. Gandy, Fundamenta Math. 61 (1967) 215-223