One of the basic problems in array design is to synthesize desired array patterns that are independent of measured array data statistics. In this thesis, we consider the desired array patterns including the maximum-gain, minimum-gain, single lookdirection and shaped patterns. Despite the different definitions of desired array patterns, it is possible to study the pattern synthesis problems in one framework based on eigen-analysis. This thesis presents original work on the following areas in synthesizing desired array patterns: (i) A target-oriented array-mode (TOAM) technique for analyzing general array pattern-synthesis systems based on eigen-analysis. (ii) An acoustical-hotspot generation method using the maximum-gain TOAM as the optimal array weight. (iii) A new analysis method using lower-gain TOAMs for deriving the optimal weights of secondary-sources in quiet-zone generation. (iv) A new method for the synthesis of single look-direction pattern and shaped array pattern based on a nonlinear optimization algorithm using TOAM series expansion. (v) A new iterative method for synthesizing single look-direction pattern and shaped array pattern with equal-level sidelobes.