A new method of the measurement of the maximal laser pulse intensity at the focal spot is suggested. The measurement
of the energies of electrons ejected from the focal spot by laser radiation is used.
The radiation emitted by an electron driven by a relativistically intense laser field comprises a set of electromagnetic
pulses with complicated spectral structure having durations much shorter than the optical cycle.
The motions of electrons driven by the fields of linearly and circularly polarized relativistically intense laser pulses are
analyzed. The treatment is based on the numerical solution of Newton's equation with the Lorentz force. The
electromagnetic radiation of an electron interacting with a laser pulse is studied. It is shown that this radiation comprises
short pulses having the attosecond range durations. An electron which is at rest initially does not follow the figure-eight
trajectories in the field of a linearly polarized laser pulse.