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When free atoms interact with intense laser fields, there are three main processes of importance: high harmonic generation (HHG), above-threshold ionization (ATI) and non-sequential double ionization (NSDI). All three of these multi-photon processes are physically strongly related to each other, they all share a common behaviour of the electron dynamics: First, an electron is ionized, then it is accelerated in the external field, and when returning to the parent ion, it can exert its kinetic energy to initialize the processes mentioned above.\n\n The subject of this thesis is the investigation of ATI and NSDI of atoms and simple molecules. Aside from two different species of matter, there are also two different kinds of laser pulses available for comparison. The femtosecond\nlasers used here differ in their specifications: one of them delivers \u201dordinary\u201c\nfemtosecond pulses, consisting of many optical cycles of the underlying electric field (many-cycle pulses), while the other one delivers extremely short pulses, only consisting of very few optical cycles (few-cycle pulses). The latter case is the reason that a new physical quantity, the absolute phase or CEO-phase (Carrier-Envelope Offset), comes into play. This quantity is defined as the relative phase of the evelope of the pulse and the underlying field. The experiments of this thesis compare the behaviour of multi-photon effects under these different conditions. It can be shown, that not only qualitatively new effects appear depending on the absolute phase, but it is also possible to gain insight into inner-atomic processes with attosecond precision.\n\n Most of the observed processes can be explained by means of an intuitive,\nsemi-classical model. Nevertheless, pure quantum-effects were also observed. One example is interference effects of ATI spectra with few-cycle pulses in analogy to the double-slit experiment of matter waves. As another example, the level-structure of the investigated atoms dominates the features of the energy distribution of the ATI-electrons.\n\n As a useful application of the discussed phase measurement, it was investigated how to apply the special features of ATI to implement a new stabilization scheme for the absolute phase of a few-cycle pulse laser system. In the frame of this work, the lasers used have been significantly improved. Those activities are also described in the thesis.