In the field of airborne earth observation there is special attention to compact, cost effective, high resolution imaging sensors. Such sensors are foreseen to play an important role in small-scale remote sensing applications, such as the monitoring of dikes, watercourses, or highways. Furthermore, such sensors are of military interest; reconnaissance tasks could be performed with small unmanned aerial vehicles (UAVs), reducing in this way the risk for one's own troops. In order to be operated from small, even unmanned, aircrafts, such systems must consume little power and be small enough to fulfill the usually strict payload requirements. Moreover, to be of interest for the civil market, cost effectiveness is mandatory. Frequency Modulated Continuous Wave (FMCW) radar systems are generally compact and relatively cheap to purchase and to exploit. They consume little power and, due to the fact that they are continuously operating, they can transmit a modest power, which makes them very interesting for military operations. Consequently, FMCW radar technology is of interest for civil and military airborne earth observation applications, specially in combination with high resolution Synthetic Aperture Radar (SAR) techniques. The novel combination of FMCW technology and SAR techniques leads to the development of a small, lightweight and cost-effective high resolution imaging sensor. SAR techniques have been successfully applied in combination with coherent pulse radars. Also the concept of synthetic aperture with FMCW sensors has already been put forward in literature, and some experimental systems have been described. However, the practical feasibility of an airborne FMCW SAR was not evident; the experimental sensors described in literature were, in fact, radars mounted on rail supports operating in ground SAR configurations and at short distances. The FMCW radars could perform measurements in each position of the synthetic aperture and then be moved to the next one. As in conventional pulse SAR systems, the stop-and-go approximation could be used; such an approximation assumes the radar platform stationary during the transmission of the electromagnetic pulses and the reception of the corresponding echoes. For airborne FMCW radars, however, the stop-and-go approximation can be not valid anymore because the platform is actually moving while continuously transmitting. A complete model for the deramped FMCW SAR signal was missing in the literature. In addition to the particular signal aspects relative to the combination of FMCW technology and SAR techniques, the use of FMCW radars for long range high resolution applications was not evident. In practical FMCW sensors, specially when using cheap components, the presence of unwanted non-linearities in the frequency modulation severely degrades the radar performances for long distances. Again, proper processing methods to overcome such limitation due to frequency non-linearities were not available to the scientific community. Therefore, the area of FMCW SAR airborne observation and related signal processing aspects was a very novel field of research. At the International Research Centre for Telecommunications and Radar (IRCTR) of the Delft University of Technology, a project was initiated to investigate the feasibility of FMCW SAR in the field of airborne earth observation and to develop proper processing algorithms to fully exploit the capability of such sensors. Within the framework of the project, the following novelties and main results have been reached and are presented in the thesis: Non-linearities correction. The author has developed a very novel processing solution, which completely solves the problem of the presence of frequency non-linearities in FMCW SAR. It corrects for the non-linearity effects for the whole range profile at once, and it allows a perfect range focussing, independently of the looking angle. The proposed method operates directly on the deramped data and it is very computationally efficient. A complete FMCW SAR signal model. The author has proposed a detailed analytical model for the FMCW SAR signal in the two-dimensional frequency domain. Based on this model, proper algorithms have been developed which guarantee the best performance when processing FMCW SAR data. Moving Target Indication (MTI) with frequency modulated CW SAR. Two SAR MTI methods are proposed. The first is based on the frequency slope diversity in the transmitted modulation by using linear triangular FMCW SAR, while the second makes use of the Doppler filtering properties of randomized SFCW modulations. First demonstration of an X-band FMCW SAR. A flight test campaign has been organized during the last part of 2005. The results were very successful. The feasibility of an operational FMCW SAR based on cheap components has been proved under practical circumstances. Thanks to the special algorithms developed, FMCW SAR images with a measured 45 cm times 25 cm resolution (including windowing) were obtained for the first time.