Multidimensional high harmonic spectroscopy is a cutting-edge technique for studying the effect of the intense low-frequency laser fields on atoms and molecules. The high energy photons, emitted by a particle as a result of the interaction with the strong laser field, carry the information about the processes in atoms and molecules, which lead to the emission. Multidimensional character of the technique allows to extract parameters of the molecular and atomic ionization dynamics, that were inaccessible before in the same experiment, such as sub-cycle ionization rates, ionization and recombination times.The Thesis presents in detail theoretical analysis of the multidimensional high harmonic generation process within semi-classical approach. Several generating field configurations are considered. The developed theoretical apparatus is then applied to describe multidimensional high harmonic spectroscopy experiments in helium. Initial analysis of the applicability of the technique for the study of multielectron dynamics in carbon dioxide is also performed.The problems, solutions to which are presented in the Thesis, are:• theoretical description of high harmonic generation in multicolor fields• analysis of the gating techniques for the extraction of the parameters of electron trajectories in high harmonic generation in He• proposition of an alternative reconstruction procedure of electron trajectory parameters, that allows one to access to all of them simultaneouslyThe main results of our work are:• Based on theoretical analysis of multidimensional high harmonic generation, we showed, that optimization of the two-dimensional harmonic 3 signal is achieved at each step of the process: ionization, propagation, dynamics in the ion and recombination• We demonstrated, that multidimensional high harmonic spectroscopy is a very sensitive tool allowing one to extract parameters of electron trajectories, such as complex ionization time and complex electron momentum, from the observed harmonic signal• We developed and applied theory to the analysis of two-color high harmonic generation experiments of He atom• We performed initial analysis of two-color HHG experiments in carbon dioxide, which was necessary for further investigation and reconstruction I thank Bettina Becker, the most helpful person in the institute or in the whole world, who made the bureaucratic problems very easy. There was no question she didn't answer and no problem she didn't solve quickly and efficiently.