The novel technique for deposition of a high quality thin films of different materials by the use of picosecond laser pulses delivered on a target with the repetition rate of several tens of megahertz is proposed. The differences of the proposed method from the conventional pulse laser deposition is due to shorter laser pulses (picosecond instead of nanosecond) and higher repetition rate which is tens of megahertz (MHz) instead of tens of hertz (Hz). The method allow us to significantly improve the quality of a film due to a decrease by nine orders of magnitude in a number of particles evaporating during a single laser pulse in comparison to that produced by nanosecond, 30 Hz lasers, thus removing a major disadvantage of laser deposition method which is the formation of particulates on the film. The use of a very high repetition rate laser also leads to a qualitatively new mode of vapor-substrate interaction. Due to the short time (10-7 - 10-8 sec) between the laser pulses a quasi-continuous laser plume is formed. The particles evaporated by the previous laser pulse and just deposited on the substrate do not cool down significantly by the time when the particles from the following laser pulse arrive, and therefore their chemical bonds are still reactive. As a result, the high repetition rate regime of evaporation allows for formation of structures on the substrate such as, for example, carbon nanotubes, polymer chains, etc. Another advantage is the opportunity of scanning the laser focal spot over different targets of different materials which allows for a deposition of multilayered films containing mono-atomic layers of different atoms. The results on ultrafast laser ablation and deposition are presented in two joint papers. In this paper (Part I) we present the theoretical justification of the ultrafast laser deposition method, calculating the vapor characteristics, evaporation and deposition rates for the optimal evaporation regime for different modes of laser- target interaction. In the second paper (Part II) the experimental results on evaporation of a graphite target, deposition of high quality diamond-like (DLC) films and the comparison of the laser plume characteristics to theory are presented.