This paper presents a geometric approach to constructing low-density parity-check (LDPC) codes, focusing on four classes of LDPC codes based on the lines and points of Euclidean and projective geometries over finite fields. These codes have good minimum distances and their Tanner graphs have a girth of 6. The paper discusses various decoding methods, including one-step majority-logic (MLG) decoding, bit flipping (BF) decoding, weighted MLG and BF decoding, a posteriori probability (APP) decoding, and iterative decoding using belief propagation (SPA). Finite-geometry LDPC codes can be decoded with linear feedback shift registers, which is an advantage not shared by other LDPC codes. The paper also explores techniques for extending and shortening these codes, achieving performance close to the Shannon limit with iterative decoding.This paper presents a geometric approach to constructing low-density parity-check (LDPC) codes, focusing on four classes of LDPC codes based on the lines and points of Euclidean and projective geometries over finite fields. These codes have good minimum distances and their Tanner graphs have a girth of 6. The paper discusses various decoding methods, including one-step majority-logic (MLG) decoding, bit flipping (BF) decoding, weighted MLG and BF decoding, a posteriori probability (APP) decoding, and iterative decoding using belief propagation (SPA). Finite-geometry LDPC codes can be decoded with linear feedback shift registers, which is an advantage not shared by other LDPC codes. The paper also explores techniques for extending and shortening these codes, achieving performance close to the Shannon limit with iterative decoding.