Dynamical properties in nanostructured and low dimensional materials 3. Magnons 3.1. Regimes of magnetization dynamics 3.2. Exchange dominated waves in films 3.3. Dipolar and dipole exchange waves in films 3.4. Experimental results for films and bilayers 3.5. Magnetic wires and stripes 3.6. Magnetic superlattices 3.7. Magnonic crystals 4. Electronic and plasmonic excitations 4.1. Electronic surface states 4.2. Graphene sheets and ribbons 4.3. Bulk dielectric functions 4.4. 2D electron gas 4.5. Bulk slab model for superlattice plasmons Preface 1. Introduction 1.1. Types of excitations or waves 1.2. Survey of types of nanostructures 1.3. Experimental techniques for dynamic properties 1.4. Theoretical methods for dynamic properties 1.5. Photonic band gaps in periodic structures 5. Polaritons 5.1. Phonon polaritons 5.2. Plasmon polaritons 5.3. Magnon polaritons 5.4. Other types of polaritons The last few years have seen dramatic advances in the growth fabrication and characterization of low dimensional materials (such as graphene) and nanostructures (such as those formed from ultrathin films wires discs and other dots ) formed either singly or in spatially periodic arrays. Most studies of these artificially engineered materials have been driven by their potential for device applications that involve smaller and smaller physical dimensions. In particular the dynamical properties of these materials are of fundamental interest for the devices that involve high frequency operation and or switching. Consequently the different excitations vibrational magnetic optical electronic and so on need to be understood from the perspective of how their properties are modified in finite structures especially on the nanometre length scale due to the presence of surfaces and interfaces. Recently the patterning of nanoelements into periodic and other arrays has become a focus of intense activity leading for example to photonic crystals and their analogues such as phononic and magnonic crystals where the control of the band gaps in the excitation spectrum is a basis for applications. The nonlinear properties of the excitations are increasingly a topic of interest as well as the linear dynamics 2. Phonons 2.1. Lattice dynamics for single surfaces and films 2.2. Elastic waves for single surfaces and films 2.3. Experimental studies 2.4. Phonons in multilayers and superlattices 2.5. Phononic crystals 6. Mixed excitations 6.1. Magnetoelastic waves 6.2. Piezoelectric waves 6.3. Ferroelectric materials 6.4. Multiferroic materials 7. Nonlinear dynamics of excitations 7.1. Fundamentals of optical and magnetic nonlinearities 7.2. Applications to non magnetic low dimensional systems 7.3. Applications to magnetic low dimensional systems Appendix. Some mathematical topics