The goal of a blind adaptive equalizer in digital communications is to compensate for the effects of intersymbol interference (ISI) without knowledge of the channel or the intended signal. Instead, only the statistics of the signal constellation are used. The constant modulus algorithm (CMA) is the most popular blind adaptive equalization algorithm used today because of its relative simplicity and effectiveness in equalizing constant-modulus signals. Although CMA does offer some equalization of non-constant modulus signals, such as quadrature amplitude modulation (QAM), it can suffer from slower convergence and higher residual ISI when considering such two-dimensional signal constellations. In this dissertation, the well-known constant-modulus algorithm (CMA) and its shortcomings when applied to QAM signals are discussed and illustrated. Then some algorithms designed to improve the performance of CMA are discussed, specifically the alphabet-matched algorithm (AMA) and the multimodulus algorithm (MMA). The use of algorithms such as AMA and MMA is intended to make a CMA-based blind adaptive equalization algorithm better suited for the equalization of QAM signals, as they, unlike CMA, consider both the amplitude and the phase of the equalizer output. Using AMA, a combined CMA+AMA cost function technique and a block decision feedback equalization (DFE) scheme are proposed, which allow for compensation of a number of the shortcomings of CMA only equalization and improve equalizer performance while adding only minimal complexity. The improvements in equalizer performance are shown through performance evaluation via simulation. It will be shown that the proposed algorithms provide faster, and sometimes more accurate, convergence, reduces residual ISI and/or increases final accuracy. -- Abstract.