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Gamma-Ray Bursts (GRBs) are short and intense pulses of soft gamma-rays. The bursts last from a fraction of a second to several hundred seconds. GRBs arrive from cosmological distances from random directions in the sky. The overall observed fluences range from 10-4ergs/cm2 to 10-7ergs/cm2 (the lower limit depends, of course, on the characteristic of the detectors and not on the bursts themselves). This corresponds to isotropic luminosity of 1051 - 1052ergs/sec, making GRBs the most luminous objects in the sky. However, we know today that most GRBs are narrowly beamed and the corresponding energies are "only" around 1051ergs [105, 291, 310], making them comparable to Supernovae in the total energy release.

The GRBs are followed by afterglow - lower energy, long lasting emission in the X-ray, optical and radio. The radio afterglow was observed in some cases several years after the bursts. The accurate afterglow positions enabled the identification of host galaxies in almost all cases when afterglow was detected and this in turn enabled the determination of the corresponding redshifts that range from 0.16 (or possibly even down to 0.0085) to 4.5. Within the host galaxies there is evidence that (long duration) GRBs arise within star forming regions and there is evidence that they follow the star formation rate.

While not all observed features are understood there is an overall agreement between the observations and the fireball model. According to the fireball model GRBs are produced when the kinetic energy of an ultra-relativistic flow is dissipated. The GRB itself is produced by internal dissipation within the flow while the afterglow is produced via external shocks with the circum-burst medium. I will focus in this review on this model.

The numerous observations of the GRB and the observations of the afterglow constrain the fireball model that describes the emitting regions. The evidence on nature of the inner engine that powers the GRB and produces the ultra-relativistic flow is however, indirect. The energetic requirements and the time scales suggest that GRB involve the formation of the black hole via a catastrophic stellar collapse event or possibly a neutron star merger. Additional indirect evidence arises from the requirement of the fireball model of long (several dozen seconds) activity of the inner engine. This hints towards an inner engine built on an accreting black hole. On the other hand, the evidence of association of GRBs with star forming regions indicates that GRBs progenitors are massive stars. Finally, the appearance of Supernova bumps in the afterglow light curve (most notably in GRB 030329) suggest association with Supernovae and stellar collapse.

I review here the theory of GRB, focusing as mentioned earlier on the fireball internal-external shocks model. I begin in Section II with a brief discussion of the observations. I turn in Section III to some generally accepted properties of GRB models - such as the essential ultra-relativistic nature of this phenomenon. Before turning to a specific discussion of the fireball model I review in Section IV several relativistic effects and in Section V the physical process, such as synchrotron emission or particle acceleration in relativistic shocks that are essential ingredients of this model. In Section VI I turn to a discussion of the prompt emission and the GRB. In Section VII I discuss modelling the afterglow emission. I consider other related phenomenon - such as TeV gamma-rays emission, high energy neutrinos, Ultra High energy cosmic rays and gravitational radiation in Section VIII. Finally, I turn in Section IX to examine different `inner engines' and various aspects related to their activity. I conclude with a discussion of open questions and observational prospects.

While writing this review I realized how large is the scope of this field and how difficult it is to cover all aspects of this interesting phenomenon. Some important aspects had to be left out. I also did not attempt to give a complete historical coverage of the field. I am sure that inadvertently I have missed many important references. I refer the reader to several other recent review papers [98, 119, 177, 231, 232, 308, 309, 416] that discuss these and other aspects of GRB theory and observations from different points of view.

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