The chapter begins with a brief introduction to sparse linear arrays. We use interval partitions to define minimum redundancy partitions and almost minimum redundancy partitions that achieve low sidelobe excitation patterns. These arrays assure that the spatial Nyquist condition is satisfied and also attempt to maximize the number of partition differences for optimized sidelobe control. Interval partitions are applied to coprime integers to generate coprime arrays. The spatial Nyquist condition and partition difference redundancy are used to develop a numerical sieve to generate arrays with low sidelobe antenna patterns. The linear Nyquist condition is generalized to two dimensions to generate 2-D sparse arrays with low sidelobe performance. Angle-of-arrival estimation methods are developed first for linear sparse arrays that satisfy the spatial Nyquist condition and then generalized to arrays that do not satisfy the spatial Nyquist condition. Finally, the methods of Ishimaru [1962] and Mitra et al. [2004, 2005] are developed to illustrate two techniques that use formulations of the uniform linear array antenna pattern to create unequally spaced arrays elements.