This paper presents a geometric approach to constructing low-density parity-check (LDPC) codes using finite geometries. Four classes of LDPC codes are constructed 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 girth 6. Finite-geometry LDPC codes can be decoded using various methods, ranging from low to high complexity and from reasonably good to very good performance. They perform well with iterative decoding and can be implemented with simple feedback shift registers, enabling linear-time encoding. These codes can be extended and shortened to obtain other good LDPC codes. The paper discusses the construction of these codes, their properties, and decoding methods, including one-step majority-logic (MLG) decoding, bit flipping (BF) decoding, and iterative decoding based on belief propagation (SPA). The paper also presents simulation results and techniques for extending and shortening finite-geometry LDPC codes. The codes are shown to achieve performance close to the Shannon limit with iterative decoding.This paper presents a geometric approach to constructing low-density parity-check (LDPC) codes using finite geometries. Four classes of LDPC codes are constructed 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 girth 6. Finite-geometry LDPC codes can be decoded using various methods, ranging from low to high complexity and from reasonably good to very good performance. They perform well with iterative decoding and can be implemented with simple feedback shift registers, enabling linear-time encoding. These codes can be extended and shortened to obtain other good LDPC codes. The paper discusses the construction of these codes, their properties, and decoding methods, including one-step majority-logic (MLG) decoding, bit flipping (BF) decoding, and iterative decoding based on belief propagation (SPA). The paper also presents simulation results and techniques for extending and shortening finite-geometry LDPC codes. The codes are shown to achieve performance close to the Shannon limit with iterative decoding.