Gamma-gay bursts (GRBs) have amazingly different time profiles. It is sometimes claimed that ``if you have seen one GRB, you have seen ... one GRB''. Statistical studies of large samples of GRBs, on the other hand, have great potential for determining some common characteristics of all GRBs. In order to find signatures of the cosmological expansion in the time profiles of GRBs, the averaged peak-aligned time profiles (ATP) of the whole available sample of (useful) GRBs (about 1300) observed by the Burst and Transient Source Experiment (BATSE) on board of the CGRO were analysed. One would expect that weak bursts (that are produced at large redshift) would show the so called ``time-dilation'' effect in their ATPs when comparing with the bright ones (presumably produced close by). It turns out that the ATP's rising slope hardly changes with brightness. This strongly rules out the simplest interpretation of the ``time-dilation'' observed for the ATP's decaying slope as being caused only by cosmological expansion. It was shown that simple bursts (dominated by a single smooth pulse) and complex bursts (consisting of overlapping pulses) have significantly different peak brightness distributions: a complex burst appears intrinsically stronger than a simple burst. This could mean that the amplitude of individual pulses is, probably, a better standard candle than the peak brightness. This can put constraints on the physical models of GRBs.
Trying to find regularities in the process generating the extremely diverse
time behaviour of GRBs, Fourier analysis was applied to 
light
curves of long bursts. A simple behavior of their power density spectra
(PDSs) was discovered: the PDS is a power law of index -5/3 plus
standard (exponentially distributed) statistical fluctuations superimposed
onto the power law. The intrinsic -5/3 power law is reproduced with high
accuracy ( 
) when averaging the PDSs of individual bursts. A
simple quantitative description of the GRB temporal behavior was thus
obtained, which has been a long sought goal. The power law is a signature
of the physical process generating GRBs. The coincidence with the
Kolmogorov law is intriguing and suggesting fully developed turbulence in
the ejecta of the GRB explosions.
The energy spectra of GRBs and their time evolution are also analyzed. The behaviour of the instantaneous (i.e., temporally resolved) spectra are of interest as they directly reflect the physics of the underlying emission processes. Especially, the spectral evolution within individual pulses is studied. The connection between the spectral and the intensity evolution has been formulated in a compact form. It was also demonstrated in what way the instantaneous spectra are related to the generally studied time-integrated pulse spectrum. It was shown how this can be used when studying observed GRB spectra.
Many detectable GRBs escaped detection (triggering) by BATSE because of too low intensity, or, so called, dead-time intervals. Such GRBs can be found in the daily count rate records which are accumulated during the full CGRO operation. Analysing the 32 Gb of archival data using an advanced triggering procedure about 1350 non-triggered GRBs were found (1.6 times more than the BATSE team found in the same data using a different technique) which doubles the available sample of GRBs. Most importantly, the efficiency of the search was measured with a novel ``test burst'' technique. A database of non-triggered GRBs is publically available at http://www.astro.su.se/groups/head/grb_archive.html. The research on GRBs is done in close collaboration with Dr. Boris Stern and Yana Tikhomirova (Moscow).