This thesis contains the complete end-to-end simulation, development, implementation, and calibration of the wide bandwidth, low-Q, Kiwi-SAS synthetic aperture sonar (SAS). Through the use of a very stable towfish, a new novel wide bandwidth transducer design, and autofocus procedures, high-resolution diffraction limited imagery is produced. As a complete system calibration was performed, this diffraction limited imagery is not only geometrically calibrated, it is also calibrated for target cross-section or target strength estimation. Is is important to note that the diffraction limited images are formed without access to any form of inertial measurement information. Previous investigations applying the synthetic aperture technique to sonar have developed processors based on exact, but inefficient, spatial-temporal domain time-delay and sum beamforming algorithms, or they have performed equivalent operations in the frequency domain using fast-correlation techniques (via the fast Fourier transform (FFT)). In this thesis, the algorithms used in the generation of synthetic aperture radar (SAR) images are derived in their wide bandwidth forms and it is shown that these more efficient algorithms can be used to form diffraction limited SAS images. Several new algorithms are developed; accelerated chirp scaling algorithm represents an efficient method for processing synthetic aperture data, while modified phase gradient autofocus and a low-Q autofocus routine based on prominent point processing are used to focus both simulated and real target data that has been corrupted by known and unknown motion or medium propagation errors.