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Doctor of Philosophy / Department of Physics / Charles L. Cocke / An underlying goal of studying atomic or molecular dynamics with short laser pulses is to reach a time scale short enough to study the evolution of the system in the time domain. In this thesis, the strong field ionization of atoms and molecules has been investigated with the highly resolved technique known as cold target recoil momentum spectroscopy (COLTRIMS). The thesis can be divided into two parts: single and double ionization. In the first part, we studied the momentum vectors of low energy electrons generated by short laser pulses of wavelengths varying from 400 to 800 nm with atomic and molecular targets with intensities in the tunneling region. Most of the structures observed in the momentum spectra of atomic and molecular targets can be explained as due to above-threshold ionization, and Freeman resonances. The most significant structure in our observed spectra is the angular structure in the lowest part of the momentum image, and this is attributed to the diffraction pattern evolved by tunneling electrons. Surprisingly, we observed that the structure produced by the electrons from high Rydberg states is independent of the internal structure of the target atom and molecules. The same work is extended to aligned molecules. The basic idea of this part of the work is to see whether the angular distribution of electrons from aligned molecules resembles the orbital structures of the molecules. The rotational revival structure was used to align the molecules. We observed pronounced energy and angular structures of the momentum images which show a dependence on the alignment of the molecule. The last part of this work mainly focuses on double ionization, i.e. the removal of two electrons from the target atoms sequentially by a short laser pulse. Measuring the complete momentum vector of Ar2+ and Ne2+, we demonstrate that these can be used to extract the angular correlation between two electrons sequentially released in the circularly polarized pulse. We demonstrate how the measurement of full momentum vectors of the doubly ionized argon and neon ions can be used to extract the time gap of the two emissions.