Since the inception of information theory by Shannon in 1948, a vast amount of research has been conducted concerning error correcting codes for communication over noisy channels. Low-Density Parity-Check (LDPC) codes represent one important class of such channel codes that are capable of closely approaching the fundamental capacity limits for suffi ciently large code lengths. This thesis especially accounts for the growing heterogeneity and the varying requirements of future (mobile) communication systems by exploring fl exible LDPC codes with respect to their code rate, length, and decoding complexity. As foundation, the traditional design process of LDPC codes is reviewed, which consists of two disciplines: - asymptotic analysis that predicts the average performance of a code ensemble and - code construction that comprises fi nite length effects and actual error correction capabilities. The following main results introduce a novel fl exible design of multi-rate and multi-length LDPC codes: - multi-rate capabilities by joint consideration of information shortening and parity puncturing, - multi-length LDPC codes by concurrent shortening and puncturing,- multi-length quasi-cyclic (QC) LDPC codes by jointly optimized lifting matrix construction. All proposed designs are based on a single mother code, enabling effi cient hardware implementations that reduce the complexity compared to current state-of-the-art methods. Furthermore, the results are combined into a multi-rate-and-multi-length LDPC code design that surpasses the fl exibility of previously known approaches. Advances in terms of fl exible decoding algorithms and their implementations are also investigated to meet the demands of the growing variety of heterogeneous devices with different computational capabilities and their manifold requirements in terms of error correction performance, computational complexity, and convergence speed.