Ions are atoms or molecules stripped of their electrons, so they can be accelerated by electric fields. They can be made to hit each other with low energy, intermediate energy, high energy, or very high energy; each energy range seeks to investigate different aspects of hadronic physics. Intermediate-energy heavy ion collisions explore the nuclei far from stability valley, the incompressibility of nuclear matter, the liquid-gas phase transition in nuclear environment, the symmetry energy far from the normal density, and other phenomena. This has been an active field of research for last four decades.This is a book for entrants in the field. It is suitable as a companion book in a graduate course. For practitioners in the field it will be useful as a reference.

This proceedings volume gives a consistent overview of various theoretical and experimental programs which study the dynamics of nucleus-nucleus collisions from low to ultra-relativistic energies. The contributions concentrate on the following topics: cold fragmentation of nuclear matter, pre-equilibrium and thermalization, thermal and chemical equilibration, fragmentation and correlations in intermediate energy collisions, dynamical properties of hot and dense nuclear matter in medium effects, resonance and strange nuclear matter, and signals of the deconfined state.High quality data obtained using experimental devices close to 4π geometries and recent theoretical developments are presented. They illustrate the significant progress made during the last few years in understanding the properties of nuclear matter in extreme conditions of pressure and temperature.This book serves as a graduate textbook and as a reference work on recent developments in this area.

Elliptic flow in ultrarelativistic heavy-ion collisions results from the hydrodynamic response to the spatial anisotropy of the initial density profile. Along-standing problem in the interpretation of flow data is that uncertainties in the initial anisotropy are mingled with uncertainties in the response. We argue that the non-Gaussianity of flow fluctuations in small systems with large fluctuations can be used to disentangle the initial state from the response. We apply this method to recent measurements of anisotropic flow in Pb+Pb and p+Pb collisions at the LHC, assuming linear response to the initial anisotropy. The response coefficient is found to decrease as the system becomes smaller and is consistent with a low value of the ratio of viscosity over entropy of [eta]/s 0.19. Deviations from linear response are studied. While they significantly change the value of the response coefficient they do not change the rate of decrease with centrality. Thus, we argue that the estimate of [eta]/s is robust against non-linear effects.

The Fourier coefficients v[2] and v[3] characterizing the anisotropy of the azimuthal distribution of charged particles produced in PbPb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV are measured with data collected by the CMS experiment. The measurements cover a broad transverse momentum range, pt= 1-100 GeV. The analysis focuses on pt> 10 GeV range, where anisotropic azimuthal distributions should reflect the path-length dependence of parton energy loss in the created medium. Results are presented in several bins of PbPb collision centrality, spanning the 60x% most central events. The v[2] coefficient is measured with the scalar product and the multiparticle cumulant methods, which have different sensitivities to the initial-state fluctuations. The values of both methods remain positive up to pt ~ 70 GeV, in all examined centrality classes. The v[3] coefficient, only measured with the scalar product method, tends to zero for pt>~ 20 GeV. Comparisons between theoretical calculations and data provide new constraints on the path-length dependence of parton energy loss in heavy ion collisions and highlight the importance of the initial-state fluctuations.