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20 reviewsThe first part of the book delivers a self‐contained exposition of differential geometry, Lie theory, representation theory, and frame theory. This material will arm the reader with the technical tools necessary to probe the discretization problem of a class of representations at a deep level. The second part of the book applies the theories laid down in the initial section to characterize a type of representations of Lie groups that can be discretized to construct frames and other basis‐like systems. For example, Lie groups with frames of translates, sampling, and interpolation spaces on Lie groups are examined. Inspired by applications in signal analysis, the book introduces novel constructions of frames possessing additional sought‐after features like boundedness, compact support, continuity, fast decay, and smoothness. The book features an extensive list of meticulously composed and concrete examples. Moreover, it draws relevant connections with ongoing dynamic research problems in frame theory, wavelet theory, time‐frequency analysis, and other related branches of harmonic analysis.